The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A292804

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A292804

Number A(n,k) of sets of nonempty words with a total of n letters over k-ary alphabet; square array A(n,k), n>=0, k>=0, read by antidiagonals.
(history; published version)

#27 by Alois P. Heinz at Fri Sep 21 17:25:59 EDT 2018

STATUS

editing

approved

#26 by Alois P. Heinz at Thu Sep 20 20:10:55 EDT 2018

EXAMPLE

A(2,2) = 5: {aa}, {ab}, {ba}, {bb}, {a,b}.

#25 by Alois P. Heinz at Thu Sep 20 17:04:37 EDT 2018

FORMULA

A(n,k) = Sum_{i=0..k} C(k,i) * A319501(n,i).

MATHEMATICA

h[n_, i_, k_] := h[n, i, k] = If[n==0, 1, If[i<1, 0, Sum[h[n-i*j, i-1, k]* Binomial[k^i, j], {j, 0, n/i}]]];

CROSSREFS

Cf. A144074, A292795, A319501.

STATUS

approved

editing

#24 by Susanna Cuyler at Sun Jun 03 07:56:51 EDT 2018

STATUS

reviewed

approved

#23 by Joerg Arndt at Sun Jun 03 07:41:18 EDT 2018

STATUS

proposed

reviewed

#22 by Jean-François Alcover at Sun Jun 03 06:57:55 EDT 2018

STATUS

editing

proposed

#21 by Jean-François Alcover at Sun Jun 03 06:57:51 EDT 2018

MATHEMATICA

h[n_, i_, k_] := h[n, i, k] = If[n==0, 1, If[i<1, 0, Sum[h[n-i*j, i-1, k]* Binomial[k^i, j], {j, 0, n/i}]]];

A[n_, k_] := h[n, n, k];

Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Jun 03 2018, from Maple *)

STATUS

approved

editing

#20 by Alois P. Heinz at Wed May 09 09:41:34 EDT 2018

STATUS

editing

approved

#19 by Alois P. Heinz at Wed May 09 09:41:30 EDT 2018

EXAMPLE

Square array A(n,k) begins:

1, 1, 1, 1, 1, 1, 1, 1, ...

0, 1, 2, 3, 4, 5, 6, 7, ...

0, 1, 5, 12, 22, 35, 51, 70, ...

0, 2, 16, 55, 132, 260, 452, 721, ...

0, 2, 42, 225, 729, 1805, 3777, 7042, ...

0, 3, 116, 927, 4000, 12376, 31074, 67592, ...

0, 4, 310, 3729, 21488, 83175, 250735, 636517, ...

0, 5, 816, 14787, 113760, 550775, 1993176, 5904746, ...

STATUS

approved

editing

#18 by Alois P. Heinz at Sun Sep 24 19:33:54 EDT 2017

STATUS

editing

approved