A254364 a(n) = 3*4^n + 10*2^n + 6*3^n + 5^n + 15.

35, 70, 182, 574, 2054, 7990, 32942, 141694, 629174, 2862790, 13275902, 62494414, 297701894, 1431677590, 6937683662, 33825224734, 165731728214, 815255212390, 4023182840222, 19905098860654, 98686897716134, 490094080827190, 2437150677449582, 12132600130570174, 60450764450513654

Offset

0,1

Comments

This is the sequence of fifth terms of "third 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 (15,-85,225,-274,120).

Formula

From Colin Barker, Jan 30 2015: (Start)

G.f.: -(2754*x^4 - 4081*x^3 + 2107*x^2 - 455*x + 35)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)).

a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5). (End)

E.g.f.: exp(x)*(exp(4*x) + 3*exp(3*x) + 6*exp(2*x) + 10*exp(x) + 15). - Elmo R. Oliveira, Sep 16 2024

Mathematica

Table[3 4^n + 10 2^n + 6 3^n + 5^n + 15, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)
LinearRecurrence[{15, -85, 225, -274, 120}, {35, 70, 182, 574, 2054}, 30] (* Harvey P. Dale, Aug 11 2016 *)

Prog

(PARI) vector(30, n, n--; 3*4^n + 10*2^n + 6*3^n + 5^n + 15) \\ Colin Barker, Jan 30 2015

Crossrefs

Cf. A062709, A254362, A254363.

Sequence in context: A353175 A229357 A376713 * A146207 A135802 A043390

Adjacent sequences: A254361 A254362 A254363 * A254365 A254366 A254367

Keyword

nonn,easy

Author

Luciano Ancora, Jan 29 2015

Status

approved