A151303 - OEIS

%I #13 Jun 02 2026 10:01:22

%S 1,2,8,30,122,508,2163,9336,40804,179887,799120,3571698,16048114,

%T 72428799,328167457,1491978164,6803716892,31110321096,142600055057,

%U 655074921487,3015313208782,13904953770666,64229950295692,297152727581176,1376720785809034,6386921652633456,29667247964299526,137964512850757605

%N Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (1, -1), (1, 0), (1, 1)}.

%H Alin Bostan and Manuel Kauers, <a href="https://arxiv.org/abs/0811.2899">Automatic Classification of Restricted Lattice Walks</a>, arXiv:0811.2899 [math.CO], 2008.

%H Mireille Bousquet-Mélou and Marni Mishna, <a href="https://arxiv.org/abs/0810.4387">Walks with small steps in the quarter plane</a>, arXiv:0810.4387 [math.CO], 2008.

%H Marni Mishna and Juan Pulido, <a href="https://arxiv.org/abs/2605.16688">On the small-step quarter plane lattice walks with a non D-finite univariate generating function</a>, arXiv:2605.16688 [math.CO], 2026. See p. 12 (Table 5).

%t 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[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

%K nonn,walk

%O 0,2

%A _Manuel Kauers_, Nov 18 2008