A099234 A trisection of 1/(1-x-x^4).

1, 1, 4, 10, 26, 69, 181, 476, 1252, 3292, 8657, 22765, 59864, 157422, 413966, 1088589, 2862617, 7527704, 19795288, 52054840, 136886433, 359964521, 946583628, 2489191330, 6545722210, 17213011605, 45264335853, 119029728628

Offset

0,3

Comments

A row of A099233.

Row sums of number triangle A116089. - Paul Barry, Feb 04 2006

Links

Michael De Vlieger, Table of n, a(n) for n = 0..2382

Hung Viet Chu, Nurettin Irmak, Steven J. Miller, Laszlo Szalay, and Sindy Xin Zhang, Schreier Multisets and the s-step Fibonacci Sequences, arXiv:2304.05409 [math.CO], 2023.

Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.

Index entries for linear recurrences with constant coefficients, signature (1,3,3,1).

Formula

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

a(n) = Sum_{k=0..n} binomial(3*(n-k), k).

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

a(n) = A003269(3n).

a(n) = Sum_{k=0..n} C(3*k,n-k) = Sum_{k=0..n} C(n,k)*C(4*k,n)/C(4*k,k). - Paul Barry, Feb 04 2006

G.f.: 1/(G(0) - x) where G(k) = 1 - (2*k+3)*x/(2*k+1 - x*(k+2)*(2*k+1)/(x*(k+2) - (k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 23 2012

Mathematica

CoefficientList[Series[1/(1-x (1+x)^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 3, 3, 1}, {1, 1, 4, 10}, 30] (* Harvey P. Dale, Jun 05 2011 *)

Crossrefs

Sequence in context: A200051 A200663 A200464 * A087222 A130583 A240048

Adjacent sequences: A099231 A099232 A099233 * A099235 A099236 A099237

Keyword

easy,nonn

Author

Paul Barry, Oct 08 2004

Status

approved