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A154222 Row sums of number triangle A154221. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A214999 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

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Last modified March 3 09:04 EST 2021. Contains 341760 sequences. (Running on oeis4.)