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
Examples
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, ...
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
- 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].
Crossrefs
Formula
Equation (32) on page 118 of the scan gives an explicit formula.