A360760 a(n) = n^16 + n^15 + n^2 + 1.

1, 4, 98309, 57395638, 5368709137, 183105468776, 3291294892069, 37980492079594, 316659348799553, 2058911320946572, 11000000000000101, 50126978032987934, 200291280469622929, 716602502197270768, 2333521433367183557, 7006302246093750226, 19599665578316398849

Offset

0,2

Comments

This polynomial over GF(2) corresponds to the cyclic redundancy check CRC-16-IBM (also called CRC-16-ANSI).

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Wikipedia, Cyclic redundancy check

Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Formula

a(n) = n^16+n^15+n^2+1.

G.f.: (-2*x^16 - 32739*x^15 - 28140955*x^14 - 2737818249*x^13 - 71190102397*x^12 - 694379743523*x^11 - 2998872587683*x^10 - 6246647694545*x^9 - 6518950156977*x^8 - 3416093767201*x^7 - 869851294713*x^6 - 99576373427*x^5 - 4406352975*x^4 - 55724249*x^3 - 98377*x^2 + 13*x - 1)/(x - 1)^17. - Chai Wah Wu, Feb 20 2023

Mathematica

Array[#^2*(#^13*(#+1)+1)+1 &, 20, 0] (* Paolo Xausa, Feb 20 2024 *)

Prog

(Python)
def A360760(n): return n**2*(n**13*(n + 1) + 1) + 1 # Chai Wah Wu, Feb 20 2023

Crossrefs

Cf. A010933.

Sequence in context: A009529 A339450 A273231 * A239021 A193151 A034209

Adjacent sequences: A360757 A360758 A360759 * A360761 A360762 A360763

Keyword

nonn,easy

Author

Darío Clavijo, Feb 19 2023

Status

approved