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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<abs(l[`if`(i=1, 0, i)-1]-l[i]+1)

       or 1<abs(l[`if`(i=n, 0, i)+1]-l[i]+1), 0,

      b(subsop(i=l[i]-1, l))), i=1..n)))(nops(l))

    end:

A:= (n, k)-> `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 August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)