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A025567 a(n) = T(n,n+1), where T is the array defined in A025564. 1
1, 4, 13, 40, 120, 356, 1050, 3088, 9069, 26620, 78133, 229384, 673699, 1979628, 5820195, 17121312, 50394579, 148413996, 437324919, 1289330520, 3803175474, 11223840012, 33139076292, 97889042384, 289276841475, 855205791076, 2529279459099 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..27.

Luca Ferrari and Emanuele Munarini, Enumeration of edges in some lattices of paths, arXiv preprint arXiv:1203.6792 [math.CO], 2012 and J. Int. Seq. 17 (2014) #14.1.5

FORMULA

G.f.: (x^2-1-sqrt(1+x)*(x^2+2*x-1)/sqrt(1-3*x))/(2*x^3). - Mark van Hoeij, May 01 2013

Conjecture: (n+3)*a(n) +4*(-n-2)*a(n-1) +2*a(n-2) +8*(n-1)*a(n-3) +3*(n-3)*a(n-4)=0. - R. J. Mathar, Apr 03 2015

Conjecture: (n-1)*(n-2)*(n+3)*a(n) -2*n*(n-2)*(n+2)*a(n-1) -3*n*(n-1)^2*a(n-2)=0. - R. J. Mathar, Apr 03 2015

MATHEMATICA

T[_, 0] = 1; T[1, 1] = 2; T[n_, k_] /; 0 <= k <= 2n := T[n, k] = T[n-1, k-2] + T[n-1, k-1] + T[n-1, k]; T[_, _] = 0;

a[n_] := T[n+1, n+3];

Array[a, 27] (* Jean-Fran├žois Alcover, Oct 30 2018 *)

PROG

(PARI)  x='x+O('x^66); Vec((x^2-1-sqrt(1+x)*(x^2+2*x-1)/sqrt(1-3*x))/(2*x^3)) \\ Joerg Arndt, May 01 2013

CROSSREFS

Pairwise sums of A014531.

Sequence in context: A027130 A027121 A238846 * A003462 A076040 A091141

Adjacent sequences:  A025564 A025565 A025566 * A025568 A025569 A025570

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)