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1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 8, 10, 8, 1, 1, 9, 18, 18, 9, 1, 1, 12, 27, 40, 27, 12, 1, 1, 13, 39, 67, 67, 39, 13, 1, 1, 16, 52, 112, 134, 112, 52, 16, 1, 1, 17, 68, 164, 246, 246, 164, 68, 17, 1, 1, 20, 85, 240, 410, 504, 410, 240, 85, 20, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k) = T(n-1, k) + T(n-1, k-1) if k is even.
T(n, n-k) = T(n, k).
Sum_{k=0..n} (-1)^k * T(n, k) = 2*[n=0] - A077957(n). (End)
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
1, 4, 1;
1, 5, 5, 1;
1, 8, 10, 8, 1;
1, 9, 18, 18, 9, 1;
1, 12, 27, 40, 27, 12, 1;
1, 13, 39, 67, 67, 39, 13, 1;
1, 16, 52, 112, 134, 112, 52, 16, 1;
1, 17, 68, 164, 246, 246, 164, 68, 17, 1;
...
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MATHEMATICA
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T[n_, k_]:= 2*Binomial[n, k] -Binomial[Mod[n, 2], Mod[k, 2]]*Binomial[Floor[n/2], Floor[k/2]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Aug 01 2023 *)
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PROG
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(Magma)
A136489:= func< n, k | 2*Binomial(n, k) - Binomial(n mod 2, k mod 2)*Binomial(Floor(n/2), Floor(k/2)) >;
(SageMath)
def A136489(n, k): return 2*binomial(n, k) - binomial(n%2, k%2)*binomial(n//2, k//2)
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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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