A171441 Expansion of g.f. (1+x)^6/(1-x).

1, 7, 22, 42, 57, 63, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64

Offset: 0

Author

Richard Choulet, Dec 09 2009

Keywords

• nonn
• easy

Comments

a(n)=2^6=64 for n>=6. We observe that this sequence is the transform of A171440 by T such that: T(u_0,u_1,u_2,u_3,u_4,u_5,...)=(u_0,u_0+u_1,u_1+u_2,u_2+u_3,u_3+u_4,...).

Also continued fraction expansion of 1+(1233212607598+5*sqrt(41))/8688482797079. - Bruno Berselli, Sep 23 2011

Examples

			a(4) = C(7,4-0) + C(7,4-2) + C(7,4-4) = 35+21+1 = 57.
		

Links

• Richard Choulet, Une nouvelle formule de combinatoire?, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A040000, A113311, A115291, A171418, A171440, A171442, A171443.

Programs

Maple

m:=7:for n from 0 to 40 do a(n):=sum('binomial(m,n-2*k)',k=0..floor(n/2)): od : seq(a(n),n=0..40);

Formula

With m=7, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).

Extensions

Definition rewritten by Bruno Berselli, Sep 23 2011