cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A036090 Centered cube numbers: (n+1)^12 + n^12.

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%I A036090 #19 Sep 08 2022 08:44:52
%S A036090 1,4097,535537,17308657,260917841,2420922961,16018069537,82560763937,
%T A036090 351149013217,1282429536481,4138428376721,12054528824977,
%U A036090 32214185570737,79991997497777,186440250265921,411221314601281
%N A036090 Centered cube numbers: (n+1)^12 + n^12.
%C A036090 Never prime, as a(n) = (2n^4 + 4n^3 + 6n^2 + 4n + 1) * (n^8 + 4n^7 + 22n^6 + 52n^5 + 69n^4 + 56n^3 + 28n^2 + 8n + 1)  Semiprime for n in {1, 2, 3, 6, 14, 16, 36, 87, 97, 109, 110, 119, 121, 163, 195, ...}. - _Jonathan Vos Post_, Aug 26 2011
%D A036090 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H A036090 Vincenzo Librandi, <a href="/A036090/b036090.txt">Table of n, a(n) for n = 0..10000</a>
%F A036090 G.f.: -(x^10 + 4082*x^9 + 474189*x^8 + 9713496*x^7 + 56604978*x^6 + 105907308*x^5 + 56604978*x^4 + 9713496*x^3 + 474189*x^2 + 4082*x + 1)*(1+x)^2 / (x-1)^13. - _R. J. Mathar_, Aug 27 2011
%t A036090 Total/@Partition[Range[0,20]^12,2,1] (* _Harvey P. Dale_, May 09 2018 *)
%o A036090 (Magma) [(n+1)^12+n^12: n in [0..20]]; // _Vincenzo Librandi_, Aug 27 2011
%Y A036090 Cf. A008456, A036088, A036089, A100267, A154535, A100266, A152913, A194155, A194185, A194216.
%K A036090 nonn
%O A036090 0,2
%A A036090 _N. J. A. Sloane_