A254028 a(n) = 2^(n+1) + 3^n + 3.

6, 10, 20, 46, 116, 310, 860, 2446, 7076, 20710, 61100, 181246, 539636, 1610710, 4815740, 14414446, 43177796, 129402310, 387944780, 1163310046, 3488881556, 10464547510, 31389448220, 94159956046, 282463090916, 847355718310

Offset: 0

Author

Luciano Ancora, Jan 22 2015

Keywords

• nonn
• easy

Comments

This is the sequence of third terms of "second partial sums of m-th powers".

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Luciano Ancora, Demonstration of formulas
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A085279, A094374, A099754.

Programs

Mathematica

Table[2^(n+1)+3^n+3,{n,0,30}] (* or *) LinearRecurrence[{6,-11,6},{6,10,20},30] (* Harvey P. Dale, Mar 27 2025 *)

PARI

a(n)=2<Charles R Greathouse IV, Jan 23 2015

PARI

Vec(-2*(13*x^2-13*x+3)/((x-1)*(2*x-1)*(3*x-1)) + O(x^100)) \\ Colin Barker, Jan 24 2015

Formula

G.f.: -2*(13*x^2-13*x+3) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 24 2015

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3). - Colin Barker, Jan 24 2015

a(n) = A085279(n+1) = 2*( A099754(n)+1 ) = 2*( A094374(n)-2 ). [Bruno Berselli, Jan 26 2015]