A114211 a(n) = (5*n^3+12*n^2+n+6)/6.

1, 4, 16, 42, 87, 156, 254, 386, 557, 772, 1036, 1354, 1731, 2172, 2682, 3266, 3929, 4676, 5512, 6442, 7471, 8604, 9846, 11202, 12677, 14276, 16004, 17866, 19867, 22012, 24306, 26754, 29361, 32132, 35072, 38186, 41479

Offset: 0

Author

Paul Barry, Nov 17 2005

Keywords

• easy
• nonn

Comments

Column 3 of A114202. Third differences are 1,1,7,5,5,5,5,5,... with g.f. (1+6x^2-2x^3)/(1-x).

Examples

			[1,3,9,5]=[1*1,3*1,3*3,1*5]=[C(3,0)*J(1),C(3,1)*J(2),C(3,2)*J(3),C(3,3)*J(4)].
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Mathematica

CoefficientList[Series[(1+6x^2-2x^3)/(1-x)^4,{x,0,75}],x]  (* Harvey P. Dale, Mar 06 2011 *)

Formula

G.f.: (1+6*x^2-2*x^3)/(1-x)^4 = (1+3*(x/(1-x))+9*(x/(1-x))^2+5*(x/(1-x))^3)/(1-x).

a(n) = sum{k=0..n, C(n, k)*C(3, k)*J(k+1)} where J(n)=A001045(n).

a(0)=1, a(n)=a(n-1)+(n-1)*(n+2)+A104249(n).