A107025 Binomial transform of the expansion of 1/(1-x^5-x^6).

1, 1, 1, 1, 1, 2, 8, 29, 85, 211, 464, 938, 1808, 3459, 6826, 14198, 30960, 69143, 154433, 340006, 734561, 1561313, 3286129, 6900097, 14542101, 30855957, 65908862, 141395972, 303745077, 651763377, 1395140215, 2978858672

Offset

0,6

Comments

In general, the binomial transform of 1/(1-x^r-x^(r+1)) is given by (1-x)^r/((1-x)^(r+1)-x^r), with a(n)=sum{k=0..floor((n+1)/2), binomial(n+k,(r+1)k)}= sum{k=0..floor((r+1)n/r), binomial(k,(r+1)n-r*k)}.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,7,-1).

Formula

G.f.: (1-x)^5/((1-x)^6-x^5); a(n)=6a(n-1)-15a(n-2)+20a(n-3)-15a(n-4)+7a(n-5)-a(n-6); a(n)=sum{k=0..floor((n+1)/2), binomial(n+k, 6k)}; a(n)=sum{k0..floor(6n/5), binomial(k, 6n-5k)}.

Crossrefs

Cf. A017837

Sequence in context: A293169 A306847 A364523 * A212385 A333882 A365760

Adjacent sequences: A107022 A107023 A107024 * A107026 A107027 A107028

Keyword

easy,nonn

Author

Paul Barry, May 09 2005

Status

approved