A097164 Expansion of (1+3x)/((1-x)(1-4x^2)).

1, 4, 8, 20, 36, 84, 148, 340, 596, 1364, 2388, 5460, 9556, 21844, 38228, 87380, 152916, 349524, 611668, 1398100, 2446676, 5592404, 9786708, 22369620, 39146836, 89478484, 156587348, 357913940, 626349396, 1431655764, 2505397588

Offset

0,2

Comments

Partial sums of A084221. a(n) = A097163(n+1)/4. Third binomial transform is A097165.

a(n+1) = 4*A097163(n). - Zerinvary Lajos, Mar 17 2008

See A133628 for an essentially identical sequence. - R. J. Mathar, Jun 08 2008

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (1,4,-4).

Formula

a(n) = 5*2^n/2 - (-2)^n/6 - 4/3;

a(n) = a(n-1) + 4a(n-2) - 4a(n-3).

G.f. ( 1+3*x ) / ( (x-1)*(2*x+1)*(2*x-1) ). - R. J. Mathar, Jul 06 2011

Maple

a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=4*a[n-2]+4 od: seq(a[n], n=1..31); # Zerinvary Lajos, Mar 17 2008

Mathematica

CoefficientList[Series[(1+3x)/((1-x)(1-4x^2)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 4, -4}, {1, 4, 8}, 50] (* Harvey P. Dale, Jul 11 2023 *)

Crossrefs

Sequence in context: A152233 A301896 A053303 * A133628 A280486 A097940

Adjacent sequences: A097161 A097162 A097163 * A097165 A097166 A097167

Keyword

easy,nonn

Author

Paul Barry, Jul 30 2004

Status

approved