A026017 - OEIS

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A026017

a(n) = number of (s(0), s(1), ..., s(2n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 2, s(2n-1) = 5. Also a(n) = T(2n-1,n-2), where T is the array defined in A026009.

1, 5, 21, 83, 319, 1209, 4550, 17068, 63954, 239666, 898909, 3375825, 12697035, 47833905, 180510210, 682341000, 2583591150, 9798281910, 37218303330, 141585223494, 539395269462, 2057771255210, 7860697923436, 30065829471048, 115135255095140, 441410428339972

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OFFSET

2,2

LINKS

Table of n, a(n) for n=2..27.

FORMULA

Expansion of (1+x^1*C^3)*C^4, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

Conjecture: (n+4)*a(n) +(-8*n-17)*a(n-1) +(19*n+1)*a(n-2) +6*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jun 20 2013

CROSSREFS

First differences of A003517.

Sequence in context: A217783 A221862 A216271 * A132310 A083319 A146041

Adjacent sequences: A026014 A026015 A026016 * A026018 A026019 A026020

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved