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Triangle read by rows: T(n,k) (n >= 2, 0 <= k <= n) = number of over-all crude totals of unbranched k-5-catapolyheptagons.
1

%I #18 Feb 08 2019 14:21:04

%S 1,2,1,4,10,8,2,16,48,52,24,4,64,224,304,200,64,8,256,1024,1664,1408,

%T 656,160,16,1024,4608,8704,8960,5440,1952,384,32,4096,20480,44032,

%U 53248,39680,18688,5440,896,64,16384,90112,217088,301056,265216,154112,59136,14464,2048,128

%N Triangle read by rows: T(n,k) (n >= 2, 0 <= k <= n) = number of over-all crude totals of unbranched k-5-catapolyheptagons.

%D 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 1.

%F T(n,k) = 2^(2*n-k-2)*(binomial(n-1,k-1)+binomial(n-2,k)/4).

%e Triangle begins:

%e [1, 2, 1],

%e [4, 10, 8, 2],

%e [16, 48, 52, 24, 4],

%e [64, 224, 304, 200, 64, 8],

%e [256, 1024, 1664, 1408, 656, 160, 16],

%e [1024, 4608, 8704, 8960, 5440, 1952, 384, 32],

%e [4096, 20480, 44032, 53248, 39680, 18688, 5440, 896, 64],

%e [16384, 90112, 217088, 301056, 265216, 154112, 59136, 14464, 2048, 128],

%e ...

%K nonn,tabf

%O 2,2

%A _N. J. A. Sloane_.

%E Revised by _N. J. A. Sloane_, Feb 08 2019