A254464 a(n) = 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28.

84, 210, 714, 2982, 14178, 73470, 404634, 2331462, 13906578, 85232910, 533860554, 3403329942, 22012307778, 144090486750, 952693102074, 6352175272422, 42655384385778, 288161867586990, 1956674663089194, 13344181547374902, 91343993647708578

Offset

0,1

Comments

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

Formula

G.f.: -6*(40188*x^6 -74058*x^5 +52931*x^4 -19005*x^3 +3647*x^2 -357*x +14) / ((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[21 2^n + 10 4^n + 15 3^n + 3 6^n + 6 5^n + 7^n + 28, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *)
LinearRecurrence[{28, -322, 1960, -6769, 13132, -13068, 5040}, {84, 210, 714, 2982, 14178, 73470, 404634}, 30] (* Harvey P. Dale, May 17 2019 *)

Prog

(PARI) vector(30, n, n--; 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28) \\ Colin Barker, Jan 31 2015

Crossrefs

Cf. A062709, A254362, A254363, A254364, A254463.

Sequence in context: A044797 A072589 A181113 * A135804 A211256 A335081

Adjacent sequences: A254461 A254462 A254463 * A254465 A254466 A254467

Keyword

nonn,easy

Author

Luciano Ancora, Jan 31 2015

Status

approved