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Search: id:A038731
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| A038731 |
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Number of columns in all directed column-convex polyominoes of area n+1. |
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+0
5
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| 1, 3, 10, 32, 99, 299, 887, 2595, 7508, 21526, 61251, 173173, 486925, 1362627, 3797374, 10543724, 29180067, 80521055, 221610563, 608468451, 1667040776, 4558234018, 12441155715, 33900136297, 92230468249, 250570010499
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.
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FORMULA
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a_n = ((2n+1)/5)F(2n+2)-((n-4)/5)F(2n+1), where the F(n)'s are the Fibonacci numbers, F(0)=0, F(1)=1
a(n)=sum(k*binom(n+k-1, 2k-2), k=1..n+1) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 11 2003
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CROSSREFS
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Row-sums of array T as in A038730.
First differences of A030267.
Sequence in context: A080406 A036682 A104270 this_sequence A053581 A092822 A017935
Adjacent sequences: A038728 A038729 A038730 this_sequence A038732 A038733 A038734
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), May 02 2000
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EXTENSIONS
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Entry improved by comments from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 14 2001
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