OFFSET
0,4
COMMENTS
The expansion of (1 + k*x^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 (1,0,0,0,0,0,4).
FORMULA
a(n) = a(n-1) + 4*a(n-7);
a(n) = Sum_{k=0..floor(n/3)} binomial(n-3k, floor(k/2))*2^k.
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 0, 4}, {1, 1, 1, 3, 3, 3, 3}, 50] (* Harvey P. Dale, Jan 26 2014 *)
PROG
(PARI) Vec((1+2*x^3)/(1-x-4*x^7)+O(x^66)) \\ Joerg Arndt, Jan 28 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 12 2004
EXTENSIONS
Name corrected by Harvey P. Dale, Jan 26 2014
STATUS
approved