A036088 Centered cube numbers: (n+1)^10 + n^10.

1, 1025, 60073, 1107625, 10814201, 70231801, 342941425, 1356217073, 4560526225, 13486784401, 35937424601, 87854788825, 199775856073, 427113146825, 865905045601, 1676162018401, 3115505528225

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Never prime, as a(n) = (2n^2 + 2n + 1) * (n^8 + 4n^7 + 18n^6 + 40n^5 + 56n^4 + 50n^3 + 27n^2 + 8n + 1), multiple of A001844(n). Semiprime for n in {2, 4, 7, 14, 19, 22, 32, 60, 65, 70, 87, 99, 102, 135, 137, ...}. - 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. A036085, A036087, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

Programs

Magma

[(n+1)^10+n^10: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

Mathematica

Total/@Partition[Range[0,20]^10,2,1] (* Harvey P. Dale, Aug 04 2019 *)

Formula

G.f.: -(x^8 + 1012*x^7 + 46828*x^6 + 408364*x^5 + 901990*x^4 + 408364*x^3 + 46828*x^2 + 1012*x + 1)*(1+x)^2 / (x-1)^11. - R. J. Mathar, Aug 27 2011