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A066709
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Triangle T(r,c) of winning binary "same game" templates.
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0
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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; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| T(r,c) is the number of winning templates with length r and minimum matching string length c; equivalently, ternary digits totaling r+c. 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
| 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
| Cf. A035615, A066345, A066346, A007318.
Sequence in context: A122542 A098542 A141343 * A174026 A108354 A146162
Adjacent sequences: A066706 A066707 A066708 * A066710 A066711 A066712
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KEYWORD
| nonn,more,tabl
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AUTHOR
| Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com), Dec 31 2001
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