A038195 Triangle read by rows: T(n,k) (n >= 2, 0 <= k <= n) = number of over-all crude totals of unbranched k-5-catapolyheptagons.

1, 2, 1, 4, 10, 8, 2, 16, 48, 52, 24, 4, 64, 224, 304, 200, 64, 8, 256, 1024, 1664, 1408, 656, 160, 16, 1024, 4608, 8704, 8960, 5440, 1952, 384, 32, 4096, 20480, 44032, 53248, 39680, 18688, 5440, 896, 64, 16384, 90112, 217088, 301056, 265216, 154112, 59136, 14464, 2048, 128

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• tabf

Examples

			Triangle begins:
[1, 2, 1],
[4, 10, 8, 2],
[16, 48, 52, 24, 4],
[64, 224, 304, 200, 64, 8],
[256, 1024, 1664, 1408, 656, 160, 16],
[1024, 4608, 8704, 8960, 5440, 1952, 384, 32],
[4096, 20480, 44032, 53248, 39680, 18688, 5440, 896, 64],
[16384, 90112, 217088, 301056, 265216, 154112, 59136, 14464, 2048, 128],
...
		

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 1.

Formula

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

Extensions

Revised by N. J. A. Sloane, Feb 08 2019