The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A151323 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)}. 0
 1, 3, 14, 67, 342, 1790, 9580, 52035, 285990, 1586298, 8864676, 49844238, 281719164, 1599314652, 9113895960, 52109150691, 298806189318, 1717855010274, 9898828072692, 57158263594458, 330662400729492, 1916134078427556, 11120825740970088, 64634042348169294, 376139362185133404, 2191569966890629380 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS A. Bostan, Computer Algebra for Lattice Path Combinatorics, Séminaire de Combinatoire Ph. Flajolet, March 28 2013. A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009. Alin Bostan, Calcul Formel pour la Combinatoire des Marches, Habilitation à Diriger des Recherches, Université Paris 13, December 2017. Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, Jean-Marie Maillard, Stieltjes moment sequences for pattern-avoiding permutations, arXiv:2001.00393 [math.CO], 2020. M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009. FORMULA G.f. appears to be (((1+2*x)/(1-6*x))^(1/4)-1)/(2*x). [From Mark van Hoeij, Nov 20 2009] Conjecture: (n+1)*a(n) -2*(2*n+1)*a(n-1) -12*(n-1)*a(n-2) = 0. - R. J. Mathar, Oct 26 2012 MATHEMATICA aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}] CROSSREFS Sequence in context: A240008 A151322 A002320 * A181662 A241478 A113140 Adjacent sequences:  A151320 A151321 A151322 * A151324 A151325 A151326 KEYWORD nonn,walk AUTHOR Manuel Kauers, Nov 18 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 18 10:56 EDT 2021. Contains 343087 sequences. (Running on oeis4.)