A180847 - OEIS

A180847

a(n) = (27^n-4^n)/23.

0, 1, 31, 853, 23095, 623821, 16844191, 454797253, 12279542215, 331547705341, 8951788306351, 241698285320053, 6525853707835735, 176198050128342061, 4757347353532344511, 128448378545641737253, 3468106220733400647655

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

The a(n+1) appear in several triangle sums of Nicomachus' table A036561, i.e Ze1(2*n), Ze1(2*n+1)/2; Ze4(3*n), Ze4(3*n+1)/3 and Ze4(3*n+2)/9. See A180662 for information about these zebra and other chess sums.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (31, -108).

FORMULA

a(n) = (27^n-4^n)/23.

G.f.: x/((27*x-1)*(4*x-1)).

a(0)=0, a(1)=1, a(n)=31*a(n-1)-108*a(n-2). [From Harvey P. Dale, Sep 01 2011]

MATHEMATICA

Table[(27^n-4^n)/23, {n, 0, 20}] (* or *) LinearRecurrence[{31, -108}, {0, 1}, 20] (* Harvey P. Dale, Sep 01 2011 *)

PROG

(PARI) a(n)=(27^n-4^n)/23 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS