A256983 Triangle read by rows: T(n,k) = number of vector partitions of n with crank k (0 <= k <= n).

1, -1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 2, 3, 2, 3, 1, 2, 1, 1, 0, 1, 4, 3, 4, 2, 3, 2, 2, 1, 1, 0, 1, 4, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 1, 7, 5, 6, 5, 5, 3, 4, 2, 2, 1, 1, 0, 1, 7, 8, 7, 7, 5, 6, 3, 4, 2, 2, 1, 1, 0, 1, 11, 9, 10, 8, 8, 6, 6, 4, 4, 2, 2, 1, 1, 0, 1, 12, 13, 11, 12, 9, 9, 7, 6, 4, 4, 2, 2, 1, 1, 0, 1

Offset

0,30

Links

Table of n, a(n) for n=0..135.

F. G. Garvan, New combinatorial interpretations of Ramanujan's partition congruences mod 5, 7 and 11, Trans. Amer. Math. Soc., 305 (1988), 47-77. MR0920146 (89b:11081).

Example

Triangle begins:
1,
-1,1,
0,0,1,
1,0,0,1,
1,0,1,0,1,
1,1,0,1,0,1,
1,1,1,1,1,0,1,
1,2,1,1,1,1,0,1,
2,2,2,1,2,1,1,0,1,
2,3,2,3,1,2,1,1,0,1,
4,3,4,2,3,2,2,1,1,0,1,
4,5,4,4,3,3,2,2,1,1,0,1,
7,5,6,5,5,3,4,2,2,1,1,0,1,
7,8,7,7,5,6,3,4,2,2,1,1,0,1,
11,9,10,8,8,6,6,4,4,2,2,1,1,0,1,
12,13,11,12,9,9,7,6,4,4,2,2,1,1,0,1,
17,15,16,13,14,10,10,7,7,4,4,...

Crossrefs

Sequence in context: A033264 A258045 A239302 * A330720 A080234 A136049

Adjacent sequences: A256980 A256981 A256982 * A256984 A256985 A256986

Keyword

sign,tabl

Author

N. J. A. Sloane, Apr 24 2015

Status

approved