A227081 Row sums of A124576.

1, 2, 8, 40, 212, 1152, 6360, 35520, 200132, 1135456, 6478088, 37128896, 213617704, 1233014720, 7136819376, 41408161920, 240758343684, 1402436532576, 8182797500328, 47814708577728, 279768031296312, 1638915078384960, 9611453035886160

Offset

0,2

Comments

The offset is chosen following the Deleham offset in A124576, not according to the less systematic offset in the definition.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Isaac DeJager, Madeleine Naquin, Frank Seidl, Colored Motzkin Paths of Higher Order, VERUM 2019.

Formula

Conjecture: 3*n*a(n) +2*(-13*n+9)*a(n-1) +4*(13*n-21)*a(n-2) +24*(-n+2)*a(n-3)=0.

a(n) ~ 2^(n-3/2)*3^(n+1/2)/sqrt(Pi*n). - Vaclav Kotesovec, Jul 06 2013

G.f.: 1/(6*x -1 +2*sqrt((2*x-1)*(6*x-1))). - Vaclav Kotesovec, Jul 06 2013

Maple

AA := proc(n, k, x, y)
    option remember;
    if k <0 or k > n then
        0 ;
    elif n = 0 then
        1;
    elif k = 0 then
        x*procname(n-1, k, x, y)+procname(n-1, 1, x, y) ;
    else
        procname(n-1, k-1, x, y)+y*procname(n-1, k, x, y)+procname(n-1, k+1, x, y) ;
    end if;
end proc:
seq(add( AA(n, k, 1, 4), k=0..n), n=0..30) ;

Mathematica

CoefficientList[Series[1/(6*x-1+2*Sqrt[(2*x-1)*(6*x-1)]), {x, 0, 30}], x] (* Vaclav Kotesovec, Jul 06 2013 *)

Prog

(PARI) x='x+O('x^30); Vec(1/(6*x -1 +2*sqrt((2*x-1)*(6*x-1)))) \\ G. C. Greubel, Nov 19 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!( 1/(6*x -1 +2*Sqrt((2*x-1)*(6*x-1))) )); // G. C. Greubel, Nov 19 2018
(Sage) s= (1/(6*x -1 +2*sqrt((2*x-1)*(6*x-1)))).series(x, 30); s.coefficients(x, sparse=False) # G. C. Greubel, Nov 19 2018

Crossrefs

Sequence in context: A139415 A119817 A025570 * A113449 A234938 A143388

Adjacent sequences: A227078 A227079 A227080 * A227082 A227083 A227084

Keyword

nonn

Author

R. J. Mathar, Jun 30 2013

Status

approved