A180846 a(n) = (81^n - 2^n)/79.

0, 1, 83, 6727, 544895, 44136511, 3575057423, 289579651327, 23455951757615, 1899932092367071, 153894499481733263, 12465454458020395327, 1009701811099652023535, 81785846699071813910431, 6624653582624816926753103

Offset: 0

Author

Johannes W. Meijer, Sep 21 2010

Keywords

• easy
• nonn

Comments

The a(n+1) appear in several triangle sums of Nicomachus's table A036561, i.e., Gi2(4*n), Gi2(4*n+1)/2, Gi2(4*n+2)/4, Gi2(4*n+3)/8 and Gi3(n). See A180662 for information about these giraffe and other chess sums.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (83,-162).

Crossrefs

Cf. A016153, A016140, A180844, A180845, A180846, A180847, A016185.

Programs

Magma

[(81^n-2^n)/79: n in [0..50]]; // Vincenzo Librandi, Apr 15 2011

Mathematica

Table[(81^n-2^n)/79,{n,0,15}] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

Formula

a(n) = (81^n - 2^n)/79.

G.f.: x/((81*x-1)*(2*x-1)).