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
KEYWORD
nonn,easy
AUTHOR
Darío Clavijo, Feb 19 2023
STATUS
approved