A132863 Expansion of 1/(1-3x*c(4x)), where c(x) is the g.f. of A000108.

1, 3, 21, 195, 2085, 24243, 297909, 3806883, 50082885, 673851795, 9229863381, 128273819523, 1804331883621, 25639360102515, 367507859864565, 5307403512554595, 77150495031376005, 1127965980470739795, 16575672566809158165, 244695925293076974915

Offset: 0

Author

Philippe Deléham, Nov 18 2007

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..830

Programs

Mathematica

CoefficientList[Series[8/(5+3Sqrt[1-16x]),{x,0,30}],x] (* Harvey P. Dale, Mar 09 2013 *)

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-1)^k*4^(n-k). - Philippe Deléham, Dec 11 2007

From Gary W. Adamson, Jul 13 2011: (Start)

a(n) = upper left term in M^n, M = an infinite square production matrix as follows:

3, 3, 0, 0, 0, 0, ...

4, 4, 4, 0, 0, 0, ...

4, 4, 4, 4, 0, 0, ...

4, 4, 4, 4, 4, 0, ...

4, 4, 4, 4, 4, 4, ...

... (End)

G.f.: 8/(5 + 3*sqrt(1-16x)). - Philippe Deléham, Oct 27 2011

Extensions

More terms from Philippe Deléham, Oct 27 2011

Corrected by Harvey P. Dale, Mar 09 2013