A275414 - OEIS

A275414

Triangle read by rows: T(n,k) is the number of multisets of k ternary words with a total of n letters.

3, 9, 6, 27, 27, 10, 81, 126, 54, 15, 243, 486, 297, 90, 21, 729, 1836, 1380, 540, 135, 28, 2187, 6561, 5994, 2763, 855, 189, 36, 6561, 23004, 24543, 13212, 4635, 1242, 252, 45, 19683, 78732, 96723, 59130, 23490, 6996, 1701, 324, 55, 59049, 265842, 368874, 253719

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OFFSET

1,1

COMMENTS

Ternary analog of A209406. Multiset transformation of A000244.

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

Index entries for triangles generated by the Multiset Transformation

FORMULA

T(n,1) = A000244(n).

T(n,k) = Sum_{c_i*N_i=n,i=1..k} binomial(T(N_i,1)+c_i-1,c_i) for 1<k<=n.

G.f.: Product_{j>=1} (1-y*x^j)^(-3^j). - Alois P. Heinz, Apr 13 2017

EXAMPLE

9 6

27 27 10

81 126 54 15

243 486 297 90 21

729 1836 1380 540 135 28

2187 6561 5994 2763 855 189 36

6561 23004 24543 13212 4635 1242 252 45

19683 78732 96723 59130 23490 6996 1701 324 55

59049 265842 368874 253719 111609 36828 9846 2232 405 66

MAPLE

b:= proc(n, i, p) option remember; `if`(p>n, 0, `if`(n=0, 1,

`if`(min(i, p)<1, 0, add(b(n-i*j, i-1, p-j)*

binomial(3^i+j-1, j), j=0..min(n/i, p)))))

end:

T:= (n, k)-> b(n$2, k):

seq(seq(T(n, k), k=1..n), n=1..14); # Alois P. Heinz, Apr 13 2017

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = If[p > n, 0, If[n == 0, 1, If[Min[i, p] < 1, 0, Sum[b[n - i*j, i-1, p - j]*Binomial[3^i + j - 1, j], {j, 0, Min[n/i, p]}]]]];

T[n_, k_] := b[n, n, k];

Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, May 19 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A144067 (row sums), A000244 (column 1), A027468 (subdiagonal ?).

Sequence in context: A223918 A224190 A223815 * A223309 A179483 A346108

Adjacent sequences: A275411 A275412 A275413 * A275415 A275416 A275417

KEYWORD

nonn,tabl

AUTHOR

R. J. Mathar, Jul 27 2016

STATUS

approved