A254463 a(n) = 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21.

56, 126, 378, 1386, 5778, 26226, 126378, 636426, 3314178, 17714466, 96660378, 536249466, 3015243378, 17141522706, 98333399178, 568324150506, 3305074833378, 19319850386946, 113420243462778, 668241096915546, 3948892688324178, 23393955029043186

Offset

0,1

Comments

This is the sequence of sixth 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 (21,-175,735,-1624,1764,-720).

Formula

G.f.: -2*(12276*x^5 -20578*x^4 +12831*x^3 -3766*x^2 +525*x -28) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Jan 31 2015

a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - Colin Barker, Jan 31 2015

Mathematica

Table[15 2^n + 6 4^n + 10 3^n + 3 5^n + 6^n + 21, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *)

Prog

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

Crossrefs

Cf. A062709, A254362, A254363, A254364, A254464.

Sequence in context: A038849 A003781 A286980 * A030443 A135803 A048452

Adjacent sequences: A254460 A254461 A254462 * A254464 A254465 A254466

Keyword

nonn,easy

Author

Luciano Ancora, Jan 31 2015

Status

approved