A098527 Expansion (1+x^3)/(1-x-x^7).

1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 7, 9, 11, 13, 16, 20, 25, 32, 41, 52, 65, 81, 101, 126, 158, 199, 251, 316, 397, 498, 624, 782, 981, 1232, 1548, 1945, 2443, 3067, 3849, 4830, 6062, 7610, 9555, 11998, 15065, 18914, 23744, 29806, 37416, 46971, 58969, 74034, 92948

Offset: 0

Author

Paul Barry, Sep 12 2004

Keywords

• easy
• nonn

Comments

The expansion of (1+kx^2)/(1-x-k^2*x^7) satisfies the recurrence a(n)=a(n-1)+k^2*a(n-7),a(0)=1,a(1)=1,a(2)=1,a(3)=k+1,a(4)=k+1, a(5)=k+1,a(6)=k+1 with a(n)=sum{k=0..floor(n/3), binomial(n-3k,floor(k/2))r^k}.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1).

Crossrefs

Cf. A097333, A098523.

Programs

Mathematica

CoefficientList[Series[(1+x^3)/(1-x-x^7),{x,0,60}],x] (* or *) LinearRecurrence[ {1,0,0,0,0,0,1},{1,1,1,2,2,2,2},60] (* Harvey P. Dale, Oct 07 2018 *)

Formula

a(n)=a(n-1)+a(n-7); a(n)=sum{k=0..floor(n/3), binomial(n-3k, floor(k/2))}.