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A026029 Number of (s(0), s(1), ..., s(2n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,....,n, s(0) = 3, s(2n) = 3. Also T(2n,n), where T is defined in A026022. 3
1, 2, 6, 20, 69, 242, 858, 3068, 11050, 40052, 145996, 534888, 1968685, 7276050, 26993490, 100490220, 375287550, 1405622460, 5278838100, 19873977240, 74994427170, 283595947284, 1074568266756, 4079184055640, 15511924233204, 59083160374952, 225384613313944 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A008619(n+1). [From Paul Barry, May 11 2009]

LINKS

Table of n, a(n) for n=0..26.

FORMULA

Expansion of (1+x^2*C^4)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

a(n) = sum{k=0..n, C(n, k)*sum{i=0..k, C(k, 2i)*A000108(i+1) }}. - Paul Barry, Jul 18 2003

a(n) = Sum_{0<=k<=3} A039599(n,k) = A000108(n)+A000245(n)+A000344(n)+A000588(n) = A026012(n)+A000588(n). [From Philippe Deléham, Nov 12 2008]

a(n) = C(2n,n)-C(2n,n-4). [From Paul Barry, May 11 2009]

Conjecture: (n+4)*a(n) +6*(-n-2)*a(n-1) +4*(2*n-1)*a(n-2)=0. - R. J. Mathar, Nov 24 2012

CROSSREFS

Sequence in context: A082679 A094854 A217782 * A078483 A163135 A047036

Adjacent sequences:  A026026 A026027 A026028 * A026030 A026031 A026032

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 22 15:12 EST 2018. Contains 299454 sequences. (Running on oeis4.)