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A066709 Triangle T(r,c) of winning binary "same game" templates. 0
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; text; internal format)
OFFSET

1,5

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)!).

LINKS

Table of n, a(n) for n=1..42.

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.

CROSSREFS

Cf. A035615, A066345, A066346, A007318.

Sequence in context: A320019 A141343 A256678 * A258051 A174026 A226075

Adjacent sequences:  A066706 A066707 A066708 * A066710 A066711 A066712

KEYWORD

nonn,more,tabl

AUTHOR

Frank Ellermann, Dec 31 2001

STATUS

approved

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Last modified October 27 03:29 EDT 2021. Contains 348270 sequences. (Running on oeis4.)