A154222 Row sums of number triangle A154221.

1, 2, 4, 8, 17, 38, 87, 200, 457, 1034, 2315, 5132, 11277, 24590, 53263, 114704, 245777, 524306, 1114131, 2359316, 4980757, 10485782, 22020119, 46137368, 96469017, 201326618, 419430427, 872415260, 1811939357, 3758096414, 7784628255, 16106127392, 33285996577

Offset: 0

Author

Paul Barry, Jan 05 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Crossrefs

Cf. A045618, A154221.

Programs

Magma

[(1/4)*(4*(n+1)+(n-1)*2^n+0^n): n in [0..35]]; // Vincenzo Librandi, Sep 07 2016

Mathematica

Join[{1},LinearRecurrence[{6, -13, 12, -4}, {2, 4, 8,17}, 25]] (* or *) Table[(1/4)*( 4*(n+1) + (n-1)*2^n + 0^n), {n,0,25}] (* G. C. Greubel, Sep 06 2016 *)

PARI

Vec((x^4-2*x^3+5*x^2-4*x+1)/((x-1)^2*(2*x-1)^2) + O(x^100)) \\ Colin Barker, Oct 11 2014

Formula

a(n) = (1/4)*( 4*(n+1) + (n-1)*2^n + 0^n).

From Colin Barker, Oct 11 2014: (Start)

a(n) = A045618(n-4) + 2^n for n>3.

a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n>4.

a(n) = (4 - 2^n + (4+2^n)*n)/4 for n>0.

G.f.: (x^4 - 2*x^3 + 5*x^2 - 4*x + 1) / ((x-1)^2*(2*x-1)^2).

(End)

E.g.f.: (1/4)*(1 + 4*(1 + x)*exp(x) + (2*x - 1)*exp(2*x)). - G. C. Greubel, Sep 06 2016

Extensions

More terms and xrefs from Colin Barker, Oct 11 2014