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A192396
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Square array T(n, k) = floor(((k+1)^n - (1+(-1)^k)/2)/2) read by antidiagonals.
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2
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0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 4, 4, 2, 0, 0, 8, 13, 8, 2, 0, 0, 16, 40, 32, 12, 3, 0, 0, 32, 121, 128, 62, 18, 3, 0, 0, 64, 364, 512, 312, 108, 24, 4, 0, 0, 128, 1093, 2048, 1562, 648, 171, 32, 4, 0, 0, 256, 3280, 8192, 7812, 3888, 1200, 256, 40, 5, 0
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OFFSET
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0,8
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COMMENTS
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T(n,k) is the number of compositions of odd natural numbers into n parts <=k.
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LINKS
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EXAMPLE
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T(2,4)=12: there are 12 compositions of odd natural numbers into 2 parts <=4
1: (0,1), (1,0);
3: (1,2), (2,1), (0,3), (3,0);
5: (1,4), (4,1), (2,3), (3,2);
7: (3,4), (4,3).
The table starts
0, 4, 13, 32, 62, 108, ... A036487;
0, 8, 40, 128, 312, 648, ... A191903;
0, 16, 121, 512, 1562, 3888, ... A191902;
. . . . ...
Antidiagonal triangle begins:
0;
0, 0;
0, 1, 0;
0, 2, 1, 0;
0, 4, 4, 2, 0;
0, 8, 13, 8, 2, 0;
0, 16, 40, 32, 12, 3, 0;
0, 32, 121, 128, 62, 18, 3, 0;
0, 64, 364, 512, 312, 108, 24, 4, 0;
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MAPLE
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A192396 := proc(n, k) (k+1)^n-(1+(-1)^k)/2 ; floor(%/2) ; end proc:
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MATHEMATICA
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T[n_, k_]:= Floor[((k+1)^n - (1+(-1)^k)/2)/2];
Table[T[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(Magma)
A192396:= func< n, k | Floor(((k+1)^n - (1+(-1)^k)/2)/2) >;
(SageMath)
def A192396(n, k): return ((k+1)^n - ((k+1)%2))//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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