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A089198 Triangle read by rows: T(n,k) (n>=0, 0<=k<=n) = number of non-squashing partitions of n into distinct parts of which the greatest is k. 0
1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 3, 3, 2, 2, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,33

LINKS

Table of n, a(n) for n=0..90.

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

FORMULA

The nonzero values of T(n, m) lie within a certain cone: T(n, m) = 0 if m < n/2 or if m > n. For m <= n <= 2m, T(n, m) = sum_{i=0}^{m-1} T(n-m, i).

For m <= n <= 2m, T(n, m) = b(n-m) if n < 2m, = b(n-m) - 1 if n = 2m, where b = A088567.

EXAMPLE

Triangle begins:

1

0 1

0 0 1

0 0 1 1

0 0 0 1 1

0 0 0 1 1 1

0 0 0 1 1 1 1

0 0 0 0 2 1 1 1

0 0 0 0 1 2 1 1 1

MATHEMATICA

T[n_, m_] := T[n, m] = Which[n==m, 1, m<n/2 || m>n, 0, True, Sum[T[n-m, i], {i, 0, m-1}]];

Table[T[n, m], {n, 0, 12}, {m, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Feb 13 2019 *)

CROSSREFS

Row sums = A088567. Rows read from right to left also give (essentially) A088567.

Sequence in context: A086009 A086010 A321929 * A059607 A176724 A015318

Adjacent sequences:  A089195 A089196 A089197 * A089199 A089200 A089201

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Dec 10 2003

STATUS

approved

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Last modified June 24 07:33 EDT 2021. Contains 345416 sequences. (Running on oeis4.)