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

%I #33 Feb 20 2024 08:08:36

%S 1,4,98309,57395638,5368709137,183105468776,3291294892069,

%T 37980492079594,316659348799553,2058911320946572,11000000000000101,

%U 50126978032987934,200291280469622929,716602502197270768,2333521433367183557,7006302246093750226,19599665578316398849

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

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

%H Paolo Xausa, <a href="/A360760/b360760.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cyclic_redundancy_check">Cyclic redundancy check</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

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

%F 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

%t Array[#^2*(#^13*(#+1)+1)+1 &, 20, 0] (* _Paolo Xausa_, Feb 20 2024 *)

%o (Python)

%o def A360760(n): return n**2*(n**13*(n + 1) + 1) + 1 # _Chai Wah Wu_, Feb 20 2023

%Y Cf. A010933.

%K nonn,easy

%O 0,2

%A _DarĂ­o Clavijo_, Feb 19 2023