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 A318191 Number A(n,k) of lattice paths from {n}^k to {0}^k using steps that decrement one component by 1 such that for each point p we have abs(p_{i}-p_{(i mod k)+1}) <= 1 and the first component used is p_1; square array A(n,k), n>=0, k>=0, read by antidiagonals. 4
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 6, 12, 4, 1, 1, 1, 24, 180, 72, 8, 1, 1, 1, 120, 4680, 5400, 432, 16, 1, 1, 1, 720, 187200, 914400, 162000, 2592, 32, 1, 1, 1, 5040, 10634400, 296438400, 178660800, 4860000, 15552, 64, 1, 1, 1, 40320, 813664800, 162273628800, 469551168000, 34907788800, 145800000, 93312, 128, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Alois P. Heinz, Antidiagonals n = 0..20, flattened EXAMPLE A(2,2) = 2^2 = 4:                     (0,1)                    /     \   (2,2)-(1,2)-(1,1)       (0,0)                    \     /                     (1,0) Square array A(n,k) begins:   1, 1,  1,     1,         1,             1,                   1, ...   1, 1,  1,     2,         6,            24,                 120, ...   1, 1,  2,    12,       180,          4680,              187200, ...   1, 1,  4,    72,      5400,        914400,           296438400, ...   1, 1,  8,   432,    162000,     178660800,        469551168000, ...   1, 1, 16,  2592,   4860000,   34907788800,     743761386086400, ...   1, 1, 32, 15552, 145800000, 6820487308800, 1178106009360998400, ... MAPLE b:= proc(l) option remember; (n-> `if`(n<2 or max(l[])=0, 1,       add(`if`(l[i]=0 or 1 `if`(k<2 or n=0, 1, b([n-1, n\$k-1])): seq(seq(A(n, d-n), n=0..d), d=0..10); CROSSREFS Columns k=0+1, 2 give: A000012, A011782. Rows n=0-2 give: A000012, A000142(n-1) for n>0, A322782/n for n>0. Main diagonal gives A320443. Cf. A227655. Sequence in context: A225200 A128706 A253586 * A208183 A214810 A257248 Adjacent sequences:  A318188 A318189 A318190 * A318192 A318193 A318194 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jan 07 2019 STATUS approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)