A016944 a(n) = (6*n + 2)^12.

4096, 68719476736, 56693912375296, 4096000000000000, 95428956661682176, 1152921504606846976, 9065737908494995456, 52654090776777588736, 244140625000000000000, 951166013805414055936, 3226266762397899821056, 9774779120406941925376, 26963771415920784510976

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

From Amiram Eldar, Mar 30 2022: (Start)

a(n) = A016933(n)^12 = A016934(n)^6 = A016935(n)^4 = A016936(n)^3 = A016938(n)^2.

a(n) = 2^12*A016788(n).

Sum_{n>=0} 1/a(n) = PolyGamma(11, 1/3)/86890185149644800. (End)

a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13). - Wesley Ivan Hurt, Feb 15 2026

Mathematica

(6*Range[0, 20]+2)^12 (* Harvey P. Dale, Aug 03 2021 *)
(* Alternative: *)
LinearRecurrence[{13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {4096, 68719476736, 56693912375296, 4096000000000000, 95428956661682176, 1152921504606846976, 9065737908494995456, 52654090776777588736, 244140625000000000000, 951166013805414055936, 3226266762397899821056, 9774779120406941925376, 26963771415920784510976}, 20] (* Harvey P. Dale, Aug 03 2021 *)

Prog

(Magma) [(6*n+2)^12: n in [0..20]]; // Vincenzo Librandi, May 05 2011

Crossrefs

Cf. A016788, A016933, A016934, A016935, A016936, A016937, A016938, A016939, A016940, A016941, A016942, A016943.

Subsequence of A008456.

Sequence in context: A016836 A013880 A016884 * A017016 A017100 A017196

Adjacent sequences: A016941 A016942 A016943 * A016945 A016946 A016947

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved