A254466 a(n) = 56*2^n + 20*4^n + 35*3^n + 4*6^n + 10*5^n + 7^n + 84.

210, 462, 1386, 5214, 22770, 110022, 571626, 3136014, 17944290, 106156182, 645091866, 4006997214, 25344197010, 162737255142, 1058251916106, 6955456112814, 46130658756930, 308314670926902, 2074188361172346, 14032607275346814, 95392686703000050

Offset

0,1

Comments

This is the sequence of seventh 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 (28,-322,1960,-6769,13132,-13068,5040).

Formula

G.f.: -6*(110440*x^6 -199272*x^5 +139840*x^4 -49405*x^3 +9345*x^2 -903*x +35) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Jan 31 2015

a(n) = 28*a(n-1) -322*a(n-2) +1960*a(n-3) -6769*a(n-4) +13132*a(n-5) -13068*a(n-6) +5040*a(n-7). - Colin Barker, Jan 31 2015

Mathematica

Table[56 2^n + 20 4^n + 35 3^n + 4 6^n + 10 5^n + 7^n + 84, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *)

Prog

(PARI) vector(30, n, n--; 56*2^n + 20*4^n + 35*3^n + 4*6^n + 10*5^n + 7^n + 84) \\ Colin Barker, Jan 31 2015

Crossrefs

Cf. A140504, A254365, A254366, A254367, A254465.

Sequence in context: A147571 A306508 A358988 * A235304 A121479 A235921

Adjacent sequences: A254463 A254464 A254465 * A254467 A254468 A254469

Keyword

nonn,easy

Author

Luciano Ancora, Jan 31 2015

Status

approved