A254366 a(n) = 4^n + 10*2^n + 4*3^n + 20.

35, 56, 112, 272, 760, 2336, 7672, 26432, 94360, 346016, 1295032, 4923392, 18943960, 73568096, 287731192, 1131465152, 4467809560, 17697740576, 70271780152, 279532195712, 1113469251160, 4439908895456, 17717752225912, 70745400779072, 282604862628760

Offset

0,1

Comments

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

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Luciano Ancora, Demonstration of formulas, page 2.

Luciano Ancora, Recurrence relations for partial sums of m-th powers

Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Formula

G.f.: -(638*x^3-777*x^2+294*x-35) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Jan 30 2015

a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - Colin Barker, Jan 30 2015

Mathematica

Table[4^n + 10*2^n + 4*3^n + 20, {n, 0, 28}] (* Michael De Vlieger, Jan 30 2015 *)

Prog

(PARI) vector(30, n, n--; 4^n + 10*2^n + 4*3^n + 20) \\ Colin Barker, Jan 30 2015

Crossrefs

Cf. A140504, A254365, A254367.

Sequence in context: A355814 A090877 A048033 * A242291 A078819 A189554

Adjacent sequences: A254363 A254364 A254365 * A254367 A254368 A254369

Keyword

nonn,easy

Author

Luciano Ancora, Jan 29 2015

Status

approved