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Search: id:A024462
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| A024462 |
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Triangle T(n,k) read by rows, arising in enumeration of catafusenes. |
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+0
5
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| 1, 1, 1, 1, 2, 1, 1, 5, 7, 3, 1, 8, 22, 24, 9, 1, 11, 46, 90, 81, 27, 1, 14, 79, 228, 351, 270, 81, 1, 17, 121, 465, 1035, 1323, 891, 243, 1, 20, 172, 828, 2430, 4428, 4860, 2916, 729, 1, 23, 232, 1344, 4914, 11718, 18144, 17496, 9477, 2187, 1, 26, 301, 2040, 8946
(list; table; graph; listen)
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OFFSET
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0,5
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REFERENCES
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S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.
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FORMULA
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T(n, k) = 3T(n-1, k-1) + T(n-1, k), starting with [1], [1, 1], [1, 2, 1].
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EXAMPLE
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1
1,1
1,2,1
1,5,7,3
1,8,22,24,9
1,11,46,90,81,27
1,14,79,228,351,270,81
1,17,121,465,1035,1323,891,243
1,20,172,828,2430,4428,4860,2916,729
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PROGRAM
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(PARI) T(n, k)=if(n<0||k<0||k>n, 0, if(n<3, [[1], [1, 1], [1, 2, 1]][n+1][k+1], 3*T(n-1, k-1)+T(n-1, k))) (from R. Stephan)
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CROSSREFS
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Cf. A038763.
Left-edge column (essentially) include A016789 and A038764. Right-edge columns (essentially) include A000244, A038765, A081892. Row sums are (essentially) A000302.
Adjacent sequences: A024459 A024460 A024461 this_sequence A024463 A024464 A024465
Sequence in context: A051012 A064644 A090210 this_sequence A049252 A098315 A036563
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KEYWORD
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tabl,nonn,easy
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AUTHOR
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njas, May 03 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000
Edited by Ralf Stephan, Jan 25 2005
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