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

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

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

Sequence in context: A069380 A006111 A183828 * A202977 A213467 A157878

Adjacent sequences: A180844 A180845 A180846 * A180848 A180849 A180850

Keyword

easy,nonn

Author

Johannes W. Meijer, Sep 21 2010

Status

approved