A238346 Triangle T(n,k) read by rows: T(n,k) is the number of compositions of n where the k-th part is the last occurrence of a largest part, n>=1, 1<=k<=n.

1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 5, 4, 1, 1, 8, 9, 8, 5, 1, 1, 14, 15, 15, 12, 6, 1, 1, 24, 27, 27, 24, 17, 7, 1, 1, 43, 47, 50, 46, 37, 23, 8, 1, 1, 77, 85, 90, 89, 75, 55, 30, 9, 1, 1, 140, 153, 165, 167, 152, 118, 79, 38, 10, 1, 1, 256, 279, 301, 313, 299, 250, 180, 110, 47, 11, 1, 1, 472, 511, 552, 582, 578, 516, 398, 267, 149, 57, 12, 1, 1

Offset

1,4

Comments

Column k=1: T(n,1) = A079500(n-1) = A007059(n).

Row sums are A011782.

Links

Joerg Arndt, Table of n, a(n) for n = 1..465 (rows 1..30, flattened)

Example

Triangle starts:
01:  1,
02:  1, 1,
03:  2, 1, 1,
04:  3, 3, 1, 1,
05:  5, 5, 4, 1, 1,
06:  8, 9, 8, 5, 1, 1,
07:  14, 15, 15, 12, 6, 1, 1,
08:  24, 27, 27, 24, 17, 7, 1, 1,
09:  43, 47, 50, 46, 37, 23, 8, 1, 1,
10:  77, 85, 90, 89, 75, 55, 30, 9, 1, 1,
11:  140, 153, 165, 167, 152, 118, 79, 38, 10, 1, 1,
12:  256, 279, 301, 313, 299, 250, 180, 110, 47, 11, 1, 1,
13:  472, 511, 552, 582, 578, 516, 398, 267, 149, 57, 12, 1, 1,
...

Crossrefs

Sequence in context: A344610 A337009 A174802 * A053538 A235803 A138201

Adjacent sequences: A238343 A238344 A238345 * A238347 A238348 A238349

Keyword

nonn,tabl

Author

Joerg Arndt and Alois P. Heinz, Feb 25 2014

Status

approved