A254367 a(n) = 5*2^(n+2) + 2^(2n+2) + 10*3^n + 5^n + 35.

70, 126, 294, 846, 2814, 10326, 40614, 168126, 723534, 3208806, 14570934, 67417806, 316645854, 1505245686, 7225414854, 34956689886, 170199537774, 832952952966, 4093454620374, 20184631056366, 99800366967294, 494533989722646, 2454868429675494

Offset

0,1

Comments

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

Formula

a(n) = 15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5). - Colin Barker, Jan 30 2015

G.f.: -2*(2972*x^4-4302*x^3+2177*x^2-462*x+35) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Jan 30 2015

Mathematica

Table[5 2^(n + 2) + 2^(2 n + 2) + 10 3^n + 5^n + 35, {n, 0, 30}] (* Vincenzo Librandi, Feb 02 2015 *)

Prog

(PARI) vector(30, n, n--; 5*2^(n+2) + 2^(2*n+2) + 10*3^n + 5^n + 35) \\ Colin Barker, Jan 30 2015
(Magma) [5*2^(n+2)+2^(2*n+2)+10*3^n+5^n+35: n in [0..30]]; // Vincenzo Librandi, Feb 02 2015

Crossrefs

Cf. A140504, A254365, A254366.

Sequence in context: A039542 A024748 A024756 * A113928 A160354 A215111

Adjacent sequences: A254364 A254365 A254366 * A254368 A254369 A254370

Keyword

nonn,easy

Author

Luciano Ancora, Jan 30 2015

Status

approved