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A135838
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Triangle read by rows: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1).
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3
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1, 2, 2, 2, 4, 2, 4, 12, 12, 4, 4, 16, 24, 16, 4, 8, 40, 80, 80, 40, 8, 8, 48, 120, 160, 120, 48, 8, 16, 112, 336, 560, 560, 336, 112, 16, 16, 128, 448, 896, 1120, 896, 448, 128, 16, 32, 288, 1152, 2688, 4032, 4032, 2688, 1152, 288, 32
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OFFSET
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1,2
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LINKS
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FORMULA
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M * Pascal's triangle as infinite lower triangular matrices, where M = a triangle with (1, 2, 2, 4, 4, 8, 8, 16, 16, ...) in the main diagonal and the rest zeros.
Sum_{k=1..n} T(n, k) = A094015(n-1).
T(n, n-k) = T(n, k).
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EXAMPLE
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First few rows of the triangle are:
1;
2, 2;
2, 4, 2;
4, 12, 12, 4;
4, 16, 24, 16, 4;
8, 40, 80, 80, 40, 8;
...
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MAPLE
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2^floor(n/2)*binomial(n-1, k-1) ;
end proc:
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MATHEMATICA
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T[n_, k_]:= 2^Floor[n/2]*Binomial[n-1, k-1];
Table[T[n, k], {n, 12}, {k, n}] //Flatten (* G. C. Greubel, Feb 07 2022 *)
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PROG
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(PARI)
A(n, k) = 2^(n\2)*binomial(n-1, k-1);
(Sage) flatten([[2^(n//2)*binomial(n-1, k-1) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Feb 07 2022
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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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