%I #31 Dec 08 2024 12:23:16

%S 1,18,115,452,1333,3254,6951,13448,24105,40666,65307,100684,149981,

%T 216958,305999,422160,571217,759714,995011,1285332,1639813,2068550,

%U 2582647,3194264,3916665,4764266,5752683,6898780,8220717,9737998

%N 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).

%H Harry J. Smith, <a href="/A061803/b061803.txt">Table of n, a(n) for n=1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = n*(6*n^4 + 10*n^2 - 1)/15. - _Dean Hickerson_, Jun 06 2001

%F G.f.: x*(1+x)^2*(1+10*x+x^2)/(1-x)^6. - _Colin Barker_, Apr 20 2012

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

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

%t 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 *)

%o (PARI) a(n) = { n*(6*n^4 + 10*n^2 - 1)/15 } \\ _Harry J. Smith_, Jul 28 2009

%Y Cf. A133824.

%K nonn,easy

%O 1,2

%A _Amarnath Murthy_, May 28 2001

%E More terms from Larry Reeves (larryr(AT)acm.org) and _Jason Earls_, May 28 2001