A323850 Irregular triangle read by rows: T(n,k) (n>=2, 0<=k<=n) = total number of unbranched k-catapolyheptagons with k pentagons and n-k heptagons.

1, 1, 1, 2, 3, 3, 1, 6, 12, 16, 6, 2, 20, 58, 82, 53, 18, 3, 72, 256, 432, 352, 174, 40, 6, 272, 1160, 2208, 2256, 1380, 498, 100, 10, 1056, 5120, 11088, 13312, 9992, 4672, 1388, 224, 20, 4160, 22560, 54432, 75344, 66448, 38600, 14840, 3644, 520, 36, 16512, 98304, 262528, 409600, 416192, 286720, 136448, 44032, 9352, 1152, 72

Offset

2,4

References

B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121. See Table 4.

Links

Table of n, a(n) for n=2..64.

B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, 1996 [Annotated scanned copy of pages 118, 119 only].

Formula

Equation (32) on page 118 of the scan gives an explicit formula.

Example

Triangle begins:
1, 1, 1,
2, 3, 3, 1,
6, 12, 16, 6, 2,
20, 58, 82, 53, 18, 3,
72, 256, 432, 352, 174, 40, 6,
272, 1160, 2208, 2256, 1380, 498, 100, 10,
1056, 5120, 11088, 13312, 9992, 4672, 1388, 224, 20,
4160, 22560, 54432, 75344, 66448, 38600, 14840, 3644, 520, 36,
16512, 98304, 262528, 409600, 416192, 286720, 136448, 44032, 9352, 1152, 72,
...

Crossrefs

The first two columns are A063376, A038177. The right-hand edge is probably either A002215 or A005418.

Sequence in context: A019798 A214734 A120653 * A236937 A323748 A116155

Adjacent sequences: A323847 A323848 A323849 * A323851 A323852 A323853

Keyword

nonn,tabf

Author

N. J. A. Sloane, Feb 09 2019

Status

approved