A025252 a(n) = (1/2)*s(n+3), where s = A025251.

0, 1, 2, 1, 6, 9, 12, 41, 60, 121, 310, 505, 1162, 2577, 4760, 11089, 23256, 47089, 107274, 223345, 476366, 1061017, 2237796, 4888313, 10745748, 23048169, 50792638, 111180265, 241786898, 534219297, 1170798128, 2570337441, 5684509232, 12503504353, 27613172114

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			G.f. = x^2 + 2*x^3 + x^4 + 6*x^5 + 9*x^6 + 12*x^7 + 41*x^8 + 60*x^9 + ...
		

Crossrefs

Cf. A025251, A160565.

Programs

Mathematica

a[ n_] := SeriesCoefficient[ (1 - x^2 - 4 x^3 - Sqrt[1 - 2 x^2 - 8 x^3 + x^4]) / (4 x^3), {x, 0, n}]; (* Michael Somos, Feb 08 2015 *)

PARI

{a(n) = if( n<1, 0, polcoeff( (-sqrt(1 - 2*x^2 - 8*x^3 + x^4 + x^4*O(x^n))) / 4, n+3))};

Formula

G.f.: (1 - x^2 - 4*x^3 - sqrt(1 - 2*x^2 - 8*x^3 + x^4)) / (4*x^3). - Michael Somos, Jun 08 2000

(n+3)*a(n) +(n+2)*a(n-1) -2*n*a(n-2) +2*(-5*n+7)*a(n-3) +(-7*n+17)*a(n-4) +(n-4)*a(n-5)=0. - R. J. Mathar, Dec 15 2013

0 = a(n)*(+a(n+1) - 20*a(n+2) - 8*a(n+3) + 7*a(n+5)) +a(n+1)*(+4*a(n+1) + 68*a(n+2) + 40*a(n+3) - 5*a(n+4) - 44*a(n+5)) + a(n+2)*(-8*a(n+2) + 4*a(n+3) + 28*a(n+4) - 8*a(n+5)) + a(n+3)*(+4*a(n+4)) + a(n+4)*(+a(n+5)) for all n>0. - Michael Somos, Feb 08 2015

a(n) = A160565(n) for all n>0. - Michael Somos, Feb 08 2015