Could I please get some help on creating a function or equation that reflects the starting number say "x" in overall resulting growth with reoccurring decay in a set pattern.
x input = y output, where z is added to y from the previous output of y to get the next number "x" "y" "z" 0 = -1,027,423,550 Where the 64th number changes 1 = -1,027,423,549 1 in this sequence and then repeats 2 = -1,027,423,552 -3 the cycle back starting at 389 infintely 3 = -1,027,423,551 1 -123 4 = -1,027,423,546 5 -123 5 = -1,027,423,545 1 -123 6 = -1,027,423,548 -3 389 7 = -1,027,423,547 1 -123 8 = -1,027,423,542 5 -123 9 = -1,027,423,541 1 -123 10 = -1,027,423,544 -3 -635 11 = -1,027,423,543 1 -123 12 = -1,027,423,538 5 -123 13 = -1,027,423,537 1 -123 14 = -1,027,423,540 -3 389 15 = -1,027,423,539 1 -123 16 = -1,027,423,534 5 -123 17 = -1,027,423,533 1 -123 18 = -1,027,423,536 -3 1413 19 = -1,027,423,535 1 -123 20 = -1,027,423,530 5 -123 21 = -1,027,423,529 1 -123 22 = -1,027,423,532 -3 23 = -1,027,423,531 1 24 = -1,027,423,526 5 25 = -1,027,423,525 1 26 = -1,027,423,528 -3 27 = -1,027,423,527 1 28 = -1,027,423,522 5 29 = -1,027,423,521 1 30 = -1,027,423,524 -3 31 = -1,027,423,523 1 32 = -1,027,423,518 5 33 = -1,027,423,517 1 34 = -1,027,423,520 -3 35 = -1,027,423,519 1 36 = -1,027,423,514 5 37 = -1,027,423,513 1 38 = -1,027,423,516 -3 39 = -1,027,423,515 1 40 = -1,027,423,510 5 41 = -1,027,423,509 1 42 = -1,027,423,512 -3 43 = -1,027,423,511 1 44 = -1,027,423,506 5 45 = -1,027,423,505 1 46 = -1,027,423,508 -3 47 = -1,027,423,507 1 48 = -1,027,423,502 5 49 = -1,027,423,501 1 50 = -1,027,423,504 -3 51 = -1,027,423,503 1 52 = -1,027,423,498 5 53 = -1,027,423,497 1 54 = -1,027,423,500 -3 55 = -1,027,423,499 1 56 = -1,027,423,494 5 57 = -1,027,423,493 1 58 = -1,027,423,496 -3 59 = -1,027,423,495 1 60 = -1,027,423,490 5 61 = -1,027,423,489 1 62 = -1,027,423,492 -3 63 = -1,027,423,491 1 64 = -1,027,423,614 -123 65 = -1,027,423,613 1 66 = -1,027,423,616 -3 67 = -1,027,423,615 1 68 = -1,027,423,610 5 69 = -1,027,423,609 1 70 = -1,027,423,612 -3 71 = -1,027,423,611 1 72 = -1,027,423,606 5 73 = -1,027,423,605 1 74 = -1,027,423,608 -3 75 = -1,027,423,607 1 76 = -1,027,423,602 5 77 = -1,027,423,601 1 78 = -1,027,423,604 -3 79 = -1,027,423,603 1 80 = -1,027,423,598 5 81 = -1,027,423,597 1 82 = -1,027,423,600 -3 83 = -1,027,423,599 1 84 = -1,027,423,594 5 85 = -1,027,423,593 1 86 = -1,027,423,596 -3 87 = -1,027,423,595 1 88 = -1,027,423,590 5 89 = -1,027,423,589 1 90 = -1,027,423,592 -3 91 = -1,027,423,591 1 92 = -1,027,423,586 5 93 = -1,027,423,585 1 94 = -1,027,423,588 -3 95 = -1,027,423,587 1 96 = -1,027,423,582 5 97 = -1,027,423,581 1 98 = -1,027,423,584 -3 99 = -1,027,423,583 1 100 = -1,027,423,578 5 101 = -1,027,423,577 1 102 = -1,027,423,580 -3 103 = -1,027,423,579 1 104 = -1,027,423,574 5 105 = -1,027,423,573 1 106 = -1,027,423,576 -3 107 = -1,027,423,575 1 108 = -1,027,423,570 5 109 = -1,027,423,569 1 110 = -1,027,423,572 -3 111 = -1,027,423,571 1 112 = -1,027,423,566 5 113 = -1,027,423,565 1 114 = -1,027,423,568 -3 115 = -1,027,423,567 1 116 = -1,027,423,562 5 117 = -1,027,423,561 1 118 = -1,027,423,564 -3 119 = -1,027,423,563 1 120 = -1,027,423,558 5 121 = -1,027,423,557 1 122 = -1,027,423,560 -3 123 = -1,027,423,559 1 124 = -1,027,423,554 5 125 = -1,027,423,553 1 126 = -1,027,423,556 -3 127 = -1,027,423,555 1 128 = -1,027,423,678 -123
Thanks ahead of time
$$y=-1027423550+x-2+2\sqrt2\sin\Bigl(\frac\pi4+x\frac\pi2\Bigr)$$