0,2

Binomial transform of A046717. Second binomial transform of A000302 (with interpolated zeros). Partial sums are A007583.

Counts closed walks of length 2n at a vertex of the cyclic graph on 4 nodes C_4. With interpolated zeros, counts closed walks of length n at a vertex of the cyclic graph on 4 nodes C_4. - Paul Barry (pbarry(AT)wit.ie), Mar 10 2004

In general, sum{k=0..n, sum{j=0..n, C(2(n-k), j)C(2k, j)r^j}} has expansion (1-(r+1)x)/(1+(r+3)x+(r-1)(r+3)x^2+(r-1)^3*x^3). - Paul Barry (pbarry(AT)wit.ie), Jun 04 2005

Index entries for sequences related to linear recurrences with constant coefficients

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

G.f.: (1-2x)/(1-4x) a(0)=1, a(1)=2, a(n)=4a(n-1), n>1. 1 followed by 4^n/2, n>0.

a(n)=(4^n+0^n)/2; E.g.f. : exp(2x)cosh(2x)=(exp(4x)+exp(0))/2. - Paul Barry (pbarry(AT)wit.ie), May 10 2003

a(n)=sum{k=0..n, C(2n, 2k) } - Paul Barry (pbarry(AT)wit.ie), May 20 2003

a(n)=A001045(2n+1)-A001045(2n-1)+0^n/2. - Paul Barry (pbarry(AT)wit.ie), Mar 10 2004

a(n)=2^n*A011782(n); a(n)=gcd(A011782(2n), A011782(2n+1)). - Paul Barry (pbarry(AT)wit.ie), Jan 12 2005

a(n)=sum{k=0..n, sum{j=0..n, C(2(n-k), j)C(2k, j)}}; - Paul Barry (pbarry(AT)wit.ie), Jun 04 2005

a(n)= Sum_{k, 0<=k<=n}A038763(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 22 2006

a(n)=int(p(n,x)^2/(pi*sqrt(x(4-x))),x,0,4) where p(n,x) is the sequence of orthogonal polynomials defined by C(2n,n): p(n,x)=(2x-4)*p(n-1,x)-4*p(n-2,x), with p(0,x)=1, p(1,x)=-2+x. - Paul Barry (pbarry(AT)wit.ie), Mar 01 2007

((2+sqrt4)^n+(2-sqrt4)^n)/2. The offset is 0. a(3)=32 [From Al Hakanson (hawkuu(AT)gmail.com), Nov 22 2008]

a(n)=A000079(n)*A011782(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008]

a(n) = A004171(n-1) = A028403(n) - A000079(n) for n >= 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jul 27 2009]

seq(ceil(count(Subset(n))*count(Composition(n))/4), n=1..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 16 2006

with(finance):seq(ceil(futurevalue(2, 3, n)), n=-1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008

Row sums of triangle A136158.

Cf. A081295, A009117. Essentially the same as A004171.

Cf. A136158.

Cf. A016742.

Sequence in context: A067897 A145682 A099752 this_sequence A004171 A009117 A160637

Adjacent sequences: A081291 A081292 A081293 this_sequence A081295 A081296 A081297

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Mar 17 2003