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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A045618, A154221.

Sequence in context: A348755 A084635 A294529 * A114199 A006196 A089796

Adjacent sequences: A154219 A154220 A154221 * A154223 A154224 A154225

Keyword

easy,nonn

Author

Paul Barry, Jan 05 2009

Extensions

More terms and xrefs from Colin Barker, Oct 11 2014

Status

approved