OFFSET
0,3
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: A=A(x) satisfies A = 1 - 2*x*A + 2*x*A^2 + x*A^3.
G.f.: A(x) = 1 + series_reversion( x/((1+x)*(1+4*x+x^2)) ).
G.f.: A(x) = (1/x)*series_reversion( x*(1-2*x + sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) ).
For n>0: a(n) = (1/n)*Sum_{j=0..n} Sum_{i=0..n-1} ( binomial(n,j) * binomial(j,i) * binomial(n-j,2*j-n-i-1) * 5^(2*n-3*j+2*i+1) ). -Vladimir Kruchinin, Dec 26 2010
MATHEMATICA
CoefficientList[1 +InverseSeries[Series[x/((1+x)*(1+4*x+x^2)), {x, 0, 30}]], x] (* G. C. Greubel, Mar 17 2021 *)
PROG
(PARI) {a(n) = polcoeff(serreverse( x*(1-2*x+sqrt((1-2*x)*(1-6*x)+x*O(x^n)))/(2*(1-2*x)))/x, n)}
(Sage)
def A118346_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( ( x/((1+x)*(1+4*x+x^2)) ).reverse() ).list()
a=A118346_list(31); [1]+a[1:] # G. C. Greubel, Mar 17 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
[1] cat Coefficients(R!( Reversion( x/((1+x)*(1+4*x+x^2)) ) )); // G. C. Greubel, Mar 17 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 26 2006
STATUS
approved