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A026016 a(n) = binomial(2*n-1, n) - binomial(2*n-1, n+3). 5
1, 3, 10, 34, 117, 407, 1430, 5070, 18122, 65246, 236436, 861764, 3157325, 11622015, 42961470, 159419670, 593636670, 2217608250, 8308432140, 31212003420, 117544456770, 443690433654, 1678353186780, 6361322162444, 24155384502452, 91882005146652 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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) = 3. Also a(n) = T(2n-1,n-1), where T is the array defined in A026009.

Number of integer lattice paths from (0,2) to (n-1,n+2) that do not cross the main diagonal.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

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

(n+3)*a(n) +(-7*n-9)*a(n-1) +2*(7*n-4)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jun 20 2013

MAPLE

a:= n-> binomial(2*n-1, n) -binomial(2*n-1, n+3): seq(a(n), n=1..27); #  Zerinvary Lajos, Dec 10 2007

MATHEMATICA

Table[Binomial[2 n - 1, n] - Binomial[2 n - 1, n + 3], {n, 1, 40}] (* Vincenzo Librandi, Jun 21 2013 *)

PROG

(MAGMA) [Binomial(2*n-1, n) - Binomial(2*n-1, n+3): n in [1..30]]; // Vincenzo Librandi, Jun 21 2013

CROSSREFS

Cf. A026009.

Sequence in context: A094832 A217778 A071725 * A109263 A136439 A178578

Adjacent sequences:  A026013 A026014 A026015 * A026017 A026018 A026019

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Better description from Darko Marinov (marinov(AT)lcs.mit.edu), May 17 2001

STATUS

approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)