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

1, 4097, 535537, 17308657, 260917841, 2420922961, 16018069537, 82560763937, 351149013217, 1282429536481, 4138428376721, 12054528824977, 32214185570737, 79991997497777, 186440250265921, 411221314601281

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

References

• B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A008456, A036088, A036089, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

Programs

Magma

[(n+1)^12+n^12: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Mathematica

Total/@Partition[Range[0,20]^12,2,1] (* Harvey P. Dale, May 09 2018 *)

Formula

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