A220163 Triangle read by rows: N_s(n,k) of spt-crank coefficients, n >= 1, k >= 0.

1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 4, 4, 3, 2, 1, 1, 5, 4, 4, 3, 2, 1, 1, 7, 7, 6, 5, 3, 2, 1, 1, 10, 9, 8, 6, 5, 3, 2, 1, 1, 13, 13, 11, 10, 7, 5, 3, 2, 1, 1, 17, 16, 15, 12, 10, 7, 5, 3, 2, 1, 1, 24, 24, 21, 18, 14, 11, 7, 5, 3, 2, 1, 1

Offset

1,7

Comments

It appears this is the same as A195011 but without its right border (for this sequence see Garvan's slides, 2012).

It appears that reversed rows converge to A000041.

Links

Table of n, a(n) for n=1..78.

George E. Andrews, Freeman J. Dyson, and Robert C. Rhoades, On the Distribution of the spt-Crank, Mathematics 2013, 1, 76-88.

G. E. Andrews, F. G. Garvan, and J. Liang, Combinatorial interpretation of congruences for the spt-function

F. G. Garvan, The smallest parts partition function, slides, 2012.

Example

1;
1,   1;
1,   1,  1;
2,   2,  1,  1;
2,   2,  2,  1,  1;
4,   4,  3,  2,  1,  1;
5,   4,  4,  3,  2,  1,  1;
7,   7,  6,  5,  3,  2,  1,  1;
10,  9,  8,  6,  5,  3,  2,  1,  1;
13, 13, 11, 10,  7,  5,  3,  2,  1,  1;
17, 16, 15, 12, 10,  7,  5,  3,  2,  1,  1;
24, 24, 21, 18, 14, 11,  7,  5,  3,  2,  1,  1;

Crossrefs

Column 1 is A195012.

Cf. A000041, A092269, A195011.

Sequence in context: A273866 A071202 A207379 * A102715 A254687 A182590

Adjacent sequences: A220160 A220161 A220162 * A220164 A220165 A220166

Keyword

nonn,tabl

Author

Omar E. Pol, Jan 15 2013

Status

approved