A097786 a(n) = 3*a(n-1) + C(n+3,3) for n > 0; a(0)=1.
1, 7, 31, 113, 374, 1178, 3618, 10974, 33087, 99481, 298729, 896551, 2690108, 8070884, 24213332, 72640812, 217923405, 653771355, 1961315395, 5883947725, 17651844946, 52955536862, 158866612886, 476599841258, 1429799526699
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-13,3).
Programs
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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 *)
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
Comments