A254369 a(n) = 15*2^n + 4^n + 5*3^n + 35.

56, 84, 156, 354, 936, 2754, 8736, 29274, 102216, 368274, 1359216, 5110794, 19495896, 75203394, 292596096, 1145977914, 4511183976, 17827536114, 70660511376, 280697078634, 1116961278456, 4450379734434, 17749154257056, 70839585900954, 282887376051336, 1130136853206354, 4516309963145136, 18052528510172874, 72171982026734616

Offset: 0

Author

Luciano Ancora, Jan 29 2015

Keywords

• nonn
• easy

Comments

This is the sequence of fourth terms of "fifth 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 (10,-35,50,-24).

Crossrefs

Cf. A168614, A254368, A254370.

Programs

Mathematica

Table[15 2^n + 4^n + 5 3^n + 35, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)
LinearRecurrence[{10,-35,50,-24},{56,84,156,354},30] (* Harvey P. Dale, Dec 04 2020 *)

PARI

vector(30, n, n--; 15*2^n + 4^n + 5*3^n + 35) \\ Colin Barker, Jan 30 2015

Formula

G.f.: -2*(533*x^3-638*x^2+238*x-28) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Jan 30 2015

a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - Colin Barker, Jan 30 2015