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%I #19 Sep 08 2022 08:44:52
%S 1,16385,4799353,273218425,6371951081,84467679721,756587236945,
%T 5076269583953,27274838966065,122876792454961,479749833583241,
%U 1663668298132105,5221294850248153,15049383211257305,40304932850948641,101250520063318561,240435420597328865
%N Centered cube numbers: a(n) = (n+1)^14 + n^14.
%C Never prime, as a(n) = (2n^2 + 2n + 1) * (n^12 + 6n^11 + 39n^10 + 140n^9 + 341n^8 + 590n^7 + 741n^6 + 680n^5 + 451n^4 + 210n^3 + 65n^2 + 12n + 1). Semiprime for n in {2, 5, 22, 24, 34, 35, 39, 84, 217, 220, 285, ...}. - _Jonathan Vos Post_, Aug 26 2011
%H Vincenzo Librandi, <a href="/A036092/b036092.txt">Table of n, a(n) for n = 0..10000</a>
%H 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 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F G.f.: -(x +1)^2*(x^12 +16368*x^11 +4520946*x^10 +193889840*x^9 +2377852335*x^8 +10465410528*x^7 +17505765564*x^6 +10465410528*x^5 +2377852335*x^4 +193889840*x^3 +4520946*x^2 +16368*x +1) / (x -1)^15. - _Colin Barker_, Feb 16 2015
%o (Magma) [(n+1)^14+n^14: n in [0..20]]; // _Vincenzo Librandi_, Aug 27 2011
%Y Cf. A000040, A036085, A036087, A036088, A036089, A036090, A036091, A100267, A154535, A100266, A152913, A194155, A194185, A194216.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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