A180844 a(n) = (27^n - 2^n)/25.

0, 1, 29, 787, 21257, 573955, 15496817, 418414123, 11297181449, 305023899379, 8235645283745, 222362422662139, 6003785411879801, 162102206120758723, 4376759565260493713, 118172508262033346635, 3190657723074900391913

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., Ca2(3*n), Ca2(3*n+1)/3, Ca2(3*n+2)/9 and Ca3(n). See A180662 for information about these camel sums and other chess sums.

Links

• Index entries for linear recurrences with constant coefficients, signature (29, -54).

Crossrefs

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

Programs

Mathematica

(#[[1]]-#[[2]])/25&/@Partition[Riffle[27^Range[0,20],2^Range[0,20]],2]  (* Harvey P. Dale, Jan 22 2011 *)

PARI

a(n) = (27^n - 2^n)/25 \\ Iain Fox, Dec 12 2017

PARI

first(n) = Vec(x/((27*x-1)*(2*x-1)) + O(x^n), -n) \\ Iain Fox, Dec 12 2017

Formula

a(n) = (27^n - 2^n)/25.

G.f.: x/((27*x-1)*(2*x-1)).