A090386 Fifth diagonal (m=4) of triangle A084938; a(n) = A084938(n+4,n) = (n^4 + 18*n^3 + 131*n^2 + 426*n)/24.

0, 24, 64, 126, 217, 345, 519, 749, 1046, 1422, 1890, 2464, 3159, 3991, 4977, 6135, 7484, 9044, 10836, 12882, 15205, 17829, 20779, 24081, 27762, 31850, 36374, 41364, 46851, 52867, 59445, 66619, 74424, 82896, 92072, 101990, 112689

Offset: 0

Author

Philippe Deléham, Jan 30 2004

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Cf. A084938 A090238.

Programs

Magma

[(n^4+18*n^3+131*n^2+426*n)/24: n in [0..40]]; // Vincenzo Librandi, Feb 24 2014

Mathematica

Table[(n^4+18n^3+131n^2+426n)/24,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,24,64,126,217},40] (* Harvey P. Dale, Feb 23 2014 *)

Formula

a(n) = A084938(n+4, n) = Sum_{k=0..4} A090238(4, k)*binomial(n, k).

a(0)=0, a(1)=24, a(2)=64, a(3)=126, a(4)=217, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Feb 23 2014

Extensions

Corrected by T. D. Noe, Nov 08 2006