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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.

%I A323850 #8 Dec 10 2023 17:55:37
%S A323850 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,
%T A323850 272,1160,2208,2256,1380,498,100,10,1056,5120,11088,13312,9992,4672,
%U A323850 1388,224,20,4160,22560,54432,75344,66448,38600,14840,3644,520,36,16512,98304,262528,409600,416192,286720,136448,44032,9352,1152,72
%N 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.
%D A323850 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.
%H A323850 B. N. Cyvin et al., <a href="/A323850/a323850.png">Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons</a>, 1996 [Annotated scanned copy of pages 118, 119 only].
%F A323850 Equation (32) on page 118 of the scan gives an explicit formula.
%e A323850 Triangle begins:
%e A323850 1, 1, 1,
%e A323850 2, 3, 3, 1,
%e A323850 6, 12, 16, 6, 2,
%e A323850 20, 58, 82, 53, 18, 3,
%e A323850 72, 256, 432, 352, 174, 40, 6,
%e A323850 272, 1160, 2208, 2256, 1380, 498, 100, 10,
%e A323850 1056, 5120, 11088, 13312, 9992, 4672, 1388, 224, 20,
%e A323850 4160, 22560, 54432, 75344, 66448, 38600, 14840, 3644, 520, 36,
%e A323850 16512, 98304, 262528, 409600, 416192, 286720, 136448, 44032, 9352, 1152, 72,
%e A323850 ...
%Y A323850 The first two columns are A063376, A038177.  The right-hand edge is probably either A002215 or A005418.
%K A323850 nonn,tabf
%O A323850 2,4
%A A323850 _N. J. A. Sloane_, Feb 09 2019