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A140586
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Triangle t(n,m) read by rows: t(n,m) = binomial(n,m) if m <= floor(n/3) or m >= floor(2n/3), otherwise t(n,m)=0.
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1
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 0, 10, 5, 1, 1, 6, 15, 0, 15, 6, 1, 1, 7, 21, 0, 35, 21, 7, 1, 1, 8, 28, 0, 0, 56, 28, 8, 1, 1, 9, 36, 84, 0, 0, 84, 36, 9, 1, 1, 10, 45, 120, 0, 0, 210, 120, 45, 10, 1
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OFFSET
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1,5
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COMMENTS
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Approximately one third of the coefficients in the middle of each row of the Pascal triangle are set to zero.
Row sums are 1, 2, 4, 8, 16, 22, 44, 93, 130, 260, 562, ...
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LINKS
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EXAMPLE
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1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 6, 4, 1;
1, 5, 0, 10, 5, 1;
1, 6, 15, 0, 15, 6, 1;
1, 7, 21,0, 35, 21, 7, 1;
1, 8, 28, 0, 0, 56, 28, 8, 1;
1, 9, 36, 84, 0, 0, 84, 36, 9, 1;
1, 10, 45, 120, 0, 0, 210, 120, 45, 10, 1;
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MAPLE
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if k <= floor(n/3) or k >= floor(2*n/3) then
binomial(n, k) ;
else
0 ;
end if;
end proc:
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MATHEMATICA
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Table[Which[m<=Floor[n/3], Binomial[n, m], m>=Floor[2 n/3], Binomial[ n, m], True, 0], {n, 0, 10}, {m, 0, n}]//Flatten (* Harvey P. Dale, May 26 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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