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A209354 Triangular array:  T(n,k) = number of partitions of n for which (maximal term)-(minimal term)=k, if 0<=k<n, and T(n,n)=1. 0
1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 1, 3, 1, 1, 0, 1, 3, 2, 3, 1, 1, 0, 1, 1, 5, 3, 3, 1, 1, 0, 1, 3, 4, 6, 3, 3, 1, 1, 0, 1, 2, 6, 6, 7, 3, 3, 1, 1, 0, 1, 3, 6, 10, 7, 7, 3, 3, 1, 1, 0, 1, 1, 9, 10, 12, 8, 7, 3, 3, 1, 1, 0, 1, 5, 6, 15, 14, 13, 8, 7, 3, 3, 1, 1, 0, 1, 1, 11, 15, 20 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

Row sums:  A000041 (number of partitions of n)

LINKS

Table of n, a(n) for n=1..95.

EXAMPLE

First ten rows:

1

0 1

1 0 1

1 1 0 1

2 1 1 0 1

1 3 1 1 0 1

3 2 3 1 1 0 1

1 5 3 3 1 1 0 1

3 4 6 3 3 1 1 0 1

2 6 6 7 3 3 1 1 0 1

Row 5 (counting the top row as row 0):

T(5,0)=1 counts [1,1,1,1,1]

T(5,1)=3 counts [2,1,1,1], [2,2,1], [3,2]

T(5,2)=1 counts [3,1,1]

T(5,3)=1 counts [4,1]

T(5,4)=0

T(5,5)=1 counts [5]

MATHEMATICA

f[n_] := IntegerPartitions[n];

p[n_, k_] := f[n][[k]];

r[n_] := Table[p[n, k], {k, 1, Length[f[n]]}]

g[n_, k_] := Max[p[n, k]] - Min[p[n, k]]; g[n_, 1] := n;

t[n_] := Table[g[n, k], {k, 1, Length[f[n]]}]

c[0, 0] = 1; c[n_, k_] := Count[t[n], k]

u = Table[c[n, k], {n, 0, 15}, {k, 0, n}];

TableForm[u] (* as an triangle *)

Flatten[u]   (* as a sequence *)

CROSSREFS

Cf. A000041.

Sequence in context: A147809 A217605 A096651 * A114640 A056890 A169590

Adjacent sequences:  A209351 A209352 A209353 * A209355 A209356 A209357

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 06 2012

STATUS

approved

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Last modified August 18 16:08 EDT 2017. Contains 290727 sequences.