A241527 a(n) = n^3 + (3^n+1)/2.

1, 3, 13, 41, 105, 247, 581, 1437, 3793, 10571, 30525, 89905, 267449, 799359, 2394229, 7177829, 21527457, 64574995, 193716077, 581137593, 1743400201, 5230185863, 15690540453, 47071601581, 141214782065, 423644320347, 1270932931741, 3812798762177, 11438396249433, 34315188706831

Offset: 0

Author

Gerasimov Sergey, Apr 24 2014

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-13,3).

Crossrefs

Cf. A000578, A007051.

Programs

Magma

[n^3 + (3^n+1)/2: n in [0..29]]; // Juri-Stepan Gerasimov, Apr 25 2014

Mathematica

Table[n^3+(3^n+1)/2,{n,0,40}] (* or *) LinearRecurrence[{7,-18,22,-13,3},{1,3,13,41,105},40] (* Harvey P. Dale, Mar 01 2024 *)

Formula

a(n) = A000578(n) + A007051(n).

G.f.: (x^4+18*x^3-10*x^2+4*x-1) / ((x-1)^4*(3*x-1)). - Colin Barker, Apr 25 2014