OFFSET
0,2
COMMENTS
Partial sums of A052150.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-13,3).
FORMULA
G.f.: 1/((1-3*x)*(1-x)^4);
a(n) = 3^(n+4)/16 - (4*n^3 + 42*n^2 + 152*n + 195)/48;
a(n) = Sum_{k=0..n} binomial(n+4, k+4)*2^k.
a(n) = 7*a(n-1) - 18*a(n-2) + 22*a(n-3) - 13*a(n-4) + 3*a(n-5); a(0) = 1, a(1)=7, a(2)=31, a(3)=113, a(4)=374. - Harvey P. Dale, Nov 26 2011
MATHEMATICA
RecurrenceTable[{a[0]==1, a[n]==3a[n-1]+Binomial[n+3, 3]}, a, {n, 30}] (* or *) LinearRecurrence[{7, -18, 22, -13, 3}, {1, 7, 31, 113, 374}, 31] (* Harvey P. Dale, Nov 26 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 24 2004
STATUS
approved