A254365 a(n) = 2^(n+2) + 3^n + 10.

15, 21, 35, 69, 155, 381, 995, 2709, 7595, 21741, 63155, 185349, 547835, 1627101, 4848515, 14479989, 43308875, 129664461, 388469075, 1164358629, 3490978715, 10468741821, 31397836835, 94176733269, 282496645355, 847422827181, 2542134263795, 7626134355909

Offset: 0

Author

Luciano Ancora, Jan 29 2015

Keywords

• nonn
• easy

Comments

This is the sequence of third 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 1.
• Luciano Ancora, Recurrence relations for partial sums of m-th powers
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A140504, A254366, A254367.

Programs

Mathematica

Table[2^(n+2) + 3^n + 10, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)

PARI

vector(30, n, n--; 2^(n+2) + 3^n + 10) \\ Colin Barker, Jan 30 2015

Formula

G.f.: -(74*x^2-69*x+15) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 30 2015

a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3). - Colin Barker, Jan 30 2015