A097788 a(n)=4a(n-1)+C(n+3,3),n>0, a(0)=1.

1, 8, 42, 188, 787, 3204, 12900, 51720, 207045, 828400, 3313886, 13255908, 53024087, 212096908, 848388312, 3393554064, 13574217225, 54296870040, 217187481490, 868749927500, 3474999711771, 13899998849108, 55599995398732

Offset: 0

Author

Paul Barry, Aug 24 2004

Keywords

• easy
• nonn

Comments

Partial sums of A052161.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-22,28,-17,4).

Programs

Mathematica

RecurrenceTable[{a[0]==1,a[n]==4a[n-1]+Binomial[n+3,3]},a,{n,30}] (* or *) LinearRecurrence[{8,-22,28,-17,4},{1,8,42,188,787},30] (* Harvey P. Dale, May 04 2014 *)

Formula

G.f.: 1/((1-4x)(1-x)^4); a(n)=4^(n+4)/81-(9n^3+90n^2+303n+350)/162; a(n)=sum{k=0..n, binomial(n+4, k+4)3^k}.

a(0)=1, a(1)=8, a(2)=42, a(3)=188, a(4)=787, a(n)=8*a(n-1)- 22*a(n-2)+ 28*a(n-3)- 17*a(n-4)+4*a(n-5). - Harvey P. Dale, May 04 2014