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
Hùng Việt Chu, Nurettin Irmak, Steven J. Miller, László Szalay, and Sindy Xin Zhang, Schreier Multisets and the s-step Fibonacci Sequences, arXiv:2304.05409 [math.CO], 2023. See also Integers (2024) Vol. 24A, Art. No. A7, p. 3.
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 08 2004
STATUS
approved