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

Author

Johannes W. Meijer, Sep 21 2010

Keywords

• easy
• nonn
• changed

Comments

For n>0, a(n) appears 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

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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). - Harvey P. Dale, Sep 01 2011