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A036089 Centered cube numbers: (n+1)^11 + n^11.

%I A036089 #22 Sep 08 2022 08:44:52
%S A036089 1,2049,179195,4371451,53022429,411625181,2340123799,10567261335,
%T A036089 39970994201,131381059609,385311670611,1028320041299,2535168764725,
%U A036089 5841725563701,12699321029039,26241941903791,51864082352049
%N A036089 Centered cube numbers: (n+1)^11 + n^11.
%C A036089 Never prime, as a(n) = (2*n+1) * (n^10 + 5*n^9 + 25*n^8 + 70*n^7 + 130*n^6 + 166*n^5 + 148*n^4 + 91*n^3 + 37*n^2 + 9*n + 1). - _Jonathan Vos Post_, Aug 26 2011
%H A036089 Vincenzo Librandi, <a href="/A036089/b036089.txt">Table of n, a(n) for n = 0..10000</a>
%H A036089 B. K. Teo and N. J. A. Sloane, <a href="http://dx.doi.org/10.1021/ic00220a025">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985), 4545-4558.
%H A036089 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A036089 From _Colin Barker_, Feb 06 2020: (Start)
%F A036089 G.f.: (1 + x)*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10) / (1 - x)^12.
%F A036089 a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>11.
%F A036089 (End)
%o A036089 (Magma) [(n+1)^11+n^11: n in [0..20]]; // _Vincenzo Librandi_, Aug 27 2011
%o A036089 (PARI) Vec((1 + x)*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10) / (1 - x)^12 + O(x^40)) \\ _Colin Barker_, Feb 06 2020
%Y A036089 Cf. A008455, A036087, A036088, A100267, A154535, A100266, A152913, A194155, A194185, A194216.
%K A036089 nonn,easy
%O A036089 0,2
%A A036089 _N. J. A. Sloane_