A254368 a(n) = 5*2^n + 3^n + 15.

21, 28, 44, 82, 176, 418, 1064, 2842, 7856, 22258, 64184, 187402, 551936, 1635298, 4864904, 14512762, 43374416, 129795538, 388731224, 1164882922, 3492027296, 10470838978, 31402031144, 94185121882, 282513422576, 847456381618, 2542201372664, 7626268573642, 22878134632256, 68633061719458, 205896500803784, 617684133702202

Offset: 0

Author

Luciano Ancora, Jan 29 2015

Keywords

• nonn
• easy

Comments

This is the sequence of third terms of "fifth partial sums of m-th powers".

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Luciano Ancora, Demonstration of formulas, page 1.
• Luciano Ancora, Recurrence relations for partial sums of m-th powers
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A168614, A254369, A254370.

Programs

Mathematica

Table[5 2^n + 3^n + 15, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)
LinearRecurrence[{6,-11,6},{21,28,44},40] (* Harvey P. Dale, Apr 26 2022 *)

PARI

vector(30, n, n--; 5*2^n + 3^n + 15) \\ Colin Barker, Jan 30 2015

Formula

G.f.: -(107*x^2-98*x+21) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 30 2015

a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3). - Colin Barker, Jan 30 2015