# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a151453 Showing 1-1 of 1 %I A151453 #7 Jan 01 2024 02:39:43 %S A151453 1,4,42,578,9166,158242,2891042,54993704,1078134132,21636311154, %T A151453 442364872960,9182624116200,193028135699066,4100926056901840, %U A151453 87917821096174026,1899625977112716534,41325695763293346504,904431694783758568086,19899310516710760870766,439903811117457581870242 %N A151453 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 0), (-1, 1), (1, -1), (1, 0), (1, 1)}. %H A151453 M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387. %t A151453 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[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}] %K A151453 nonn,walk %O A151453 0,2 %A A151453 _Manuel Kauers_, Nov 18 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE