A180845 a(n) = (16^n-3^n)/13

0, 1, 19, 313, 5035, 80641, 1290499, 20648713, 330381595, 5286112081, 84577812979, 1353245066713, 21651921244555, 346430740444321, 5542891848703459, 88686269584038313, 1418980313358961915

Offset

0,3

Comments

The a(n+1) appear in several triangle sums of Nicomachus' table A036561, i.e Gi1(4*n), Gi1(4*n+1)/2, Gi1(4*n+2)/4, Gi1(4*n+3)/8 and Gi4(n). See A180662 for information about these giraffe and other chess sums.

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (19, -48).

Formula

a(n) = (16^n-3^n)/13

G.f.: x/((16*x-1)*(3*x-1))

Mathematica

Table[(16^n-3^n)/13, {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)

Crossrefs

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

Sequence in context: A370318 A032631 A142430 * A138943 A111420 A166965

Adjacent sequences: A180842 A180843 A180844 * A180846 A180847 A180848

Keyword

easy,nonn

Author

Johannes W. Meijer, Sep 21 2010

Status

approved