A036092 Centered cube numbers: a(n) = (n+1)^14 + n^14.

1, 16385, 4799353, 273218425, 6371951081, 84467679721, 756587236945, 5076269583953, 27274838966065, 122876792454961, 479749833583241, 1663668298132105, 5221294850248153, 15049383211257305, 40304932850948641, 101250520063318561, 240435420597328865

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
• Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Crossrefs

Cf. A000040, A036085, A036087, A036088, A036089, A036090, A036091, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

Programs

Magma

[(n+1)^14+n^14: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Formula

G.f.: -(x +1)^2*(x^12 +16368*x^11 +4520946*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +4520946*x^2 +16368*x +1) / (x -1)^15. - Colin Barker, Feb 16 2015