A036087 Centered cube numbers: a(n) = (n+1)^9 + n^9.

1, 513, 20195, 281827, 2215269, 12030821, 50431303, 174571335, 521638217, 1387420489, 3357947691, 7517728043, 15764279725, 31265546157, 59104406159, 107162836111, 187307353233, 316947166865

Offset

0,2

Comments

Never prime nor semiprime, as a(n) = (2n+1) * (n^2 + n + 1) * (n^6 + 3n^5 + 12n^4 + 19n^3 + 15n^2 + 6n + 1). - Jonathan Vos Post, Aug 26 2011

Triprimes (A014612) if n = 2, 5, 6, 14, 21, 75, 90, ... - R. J. Mathar, Aug 27 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

Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Formula

a(n) = A001017(n+1) + A001017(n).

G.f.: (1+x)*(x^8 + 502*x^7 + 14608*x^6 + 88234*x^5 + 156190*x^4 + 88234*x^3 + 14608*x^2 + 502*x + 1) / (x-1)^10. - R. J. Mathar, Aug 27 2011

Mathematica

Total/@Partition[Range[0, 20]^9, 2, 1] (* Harvey P. Dale, Jan 31 2015 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 513, 20195, 281827, 2215269, 12030821, 50431303, 174571335, 521638217, 1387420489}, 20] (* Harvey P. Dale, Jan 21 2023 *)

Prog

(Magma) [(n+1)^9+n^9: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011
(PARI) a(n)=(n+1)^9+n^9 \\ Charles R Greathouse IV, Jan 31 2017

Crossrefs

Cf. A036085, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

Sequence in context: A017681 A013957 A294304 * A007487 A023878 A301553

Adjacent sequences: A036084 A036085 A036086 * A036088 A036089 A036090

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved