OFFSET
0,2
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
FORMULA
a(0)=0, a(1)=6, a(2)=22, a(3)=60, a(4)=142, a(5)=305, a(6)= 607, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+a(n-7). - Harvey P. Dale, Jun 28 2011
G.f.: (2*x^6-11*x^5+26*x^4-32*x^3+20*x^2-6*x)/(x-1)^7. - Harvey P. Dale, Jun 28 2011
MATHEMATICA
Table[Binomial[n+5, 6]+Binomial[n+3, 3]+Binomial[n+2, 3]+ Binomial[n-1, 1], {n, 0, 50}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 6, 22, 60, 142, 305, 607}, 51] (* Harvey P. Dale, Jun 28 2011 *)
PROG
(PARI) a(n)=n*(n^5+15*n^4+85*n^3+465*n^2+1354*n+2400)/720 \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
D. G. Rogers, May 07 2005
STATUS
approved