A061803 Sum of n-th row of triangle of 4th powers: 1; 1 16 1; 1 16 81 16 1; 1 16 81 256 81 16 1; ... (cf. A133824).

1, 18, 115, 452, 1333, 3254, 6951, 13448, 24105, 40666, 65307, 100684, 149981, 216958, 305999, 422160, 571217, 759714, 995011, 1285332, 1639813, 2068550, 2582647, 3194264, 3916665, 4764266, 5752683, 6898780, 8220717, 9737998

Offset: 1

Author

Amarnath Murthy, May 28 2001

Keywords

• nonn
• easy

Examples

			a(3) = 115 = 1 + 16 + 81 + 16 + 1
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A133824.

Programs

Mathematica

Table[Total[2Range[n-1]^4]+n^4,{n,30}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,18,115,452,1333,3254},30] (* Harvey P. Dale, Aug 23 2016 *)

PARI

a(n) = { n*(6*n^4 + 10*n^2 - 1)/15 } \\ Harry J. Smith, Jul 28 2009

Formula

a(n) = n*(6*n^4 + 10*n^2 - 1)/15. - Dean Hickerson, Jun 06 2001

G.f.: x*(1+x)^2*(1+10*x+x^2)/(1-x)^6. - Colin Barker, Apr 20 2012

E.g.f.: exp(x)*x*(15 + 120*x + 160*x^2 + 60*x^3 + 6*x^4)/15. - Stefano Spezia, Dec 08 2024

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, May 28 2001