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Search: id:A066709
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| A066709 |
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Triangle T(r,c) of winning binary "same game" templates. |
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1
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| 1, 0, 1, 1, 2, 1, 0, 2, 4, 1, 1, 5, 8, 5, 1, 0, 3, 14, 15, 6, 1, 1, 9, 25, 32, 21, 7, 1, 0, 4, 32, 62, 56, 28, 8, 1, 1, 14, 56, 109, 122, 84
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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T(r,c) is the number of winning templates with length r and total r+c of ternary digits. For a definition and row sums 1,1,4,7,20, etc. see A066345. For antidiagonal sums 1,0,2,2,4,9, etc. see A066346. A035615(n)= 2 *sum( r=1 to n-1, c=1 to min(r,n-r): T(r,c) *P(n-r,c)), see A007318 for P(n-r,c)= C(n-r-1,c-1)= (n-r-1)!/((n-r-c-2)!*(c-1)!).
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EXAMPLE
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Rows: 1; 0,1; 1,2,2; 0,2,4,1; 1,5,8,5,1; 0,3,14,15,6,1; ...
a(17)= T(6,2)= 3 winning templates with length 6 and total 8= 6+2: 211211, 121121, 112112.
A035615(6)= 2*( 1*1+0*1+1*3+1*1+2*2+1*1+1*1+0*1+2*1+1*1 )= 2*13= 26.
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CROSSREFS
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Cf. A035615, A066345, A066346, A007318.
Sequence in context: A122542 A098542 A141343 this_sequence A108354 A146162 A147702
Adjacent sequences: A066706 A066707 A066708 this_sequence A066710 A066711 A066712
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KEYWORD
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nonn,more,tabl
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AUTHOR
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frank.ellermann(AT)t-online.de, Dec 31 2001
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