A116409 Expansion of (1-x-2x^2+sqrt(1-2x-3x^2))/(2(1-x)(1-2x-3x^2)).

1, 2, 5, 13, 36, 102, 294, 855, 2502, 7352, 21670, 64021, 189489, 561680, 1666955, 4952243, 14725010, 43815836, 130462322, 388670993, 1158491411, 3454558976, 10305303341, 30752447207, 91798204811, 274101391202, 818652308999

Offset: 0

Author

Paul Barry, Feb 13 2006

Keywords

• easy
• nonn

Comments

Row sums of A116407. Binomial transform of A116406.

Crossrefs

Cf. A116410.

Formula

Conjecture: n*a(n) +2*(-3*n+2)*a(n-1) +2*(4*n-5)*a(n-2) +6*(n-2)*a(n-3) +9*(-n+2)*a(n-4)=0. - R. J. Mathar, Nov 11 2014

a(n) ~ 3^n/4 * (1 + 3*sqrt(3/(Pi*n))/2). - Vaclav Kotesovec, May 30 2016