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A132735
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Triangle T(n,k) = binomial(n,k) + 1 with T(n,0) = T(n,n) = 1, read by rows.
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5
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1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 5, 7, 5, 1, 1, 6, 11, 11, 6, 1, 1, 7, 16, 21, 16, 7, 1, 1, 8, 22, 36, 36, 22, 8, 1, 1, 9, 29, 57, 71, 57, 29, 9, 1, 1, 10, 37, 85, 127, 127, 85, 37, 10, 1, 1, 11, 46, 121, 211, 253, 211, 121, 46, 11, 1, 1, 12, 56, 166, 331, 463, 463, 331, 166, 56, 12, 1
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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) = A007318(n,k) + 1 - A103451(n,k), an infinite lower triangular matrix.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
1, 3, 1;
1, 4, 4, 1;
1, 5, 7, 5, 1;
1, 6, 11, 11, 6, 1;
1, 7, 16, 21, 16, 7, 1;
...
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MATHEMATICA
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T[n_, k_]:= If[k==0||k==n, 1, Binomial[n, k] +1];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 14 2021 *)
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PROG
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(Sage)
def T(n, k): return 1 if (k==0 or k==n) else binomial(n, k) + 1
flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 14 2021
(Magma)
T:= func< n, k | k eq 0 or k eq n select 1 else Binomial(n, k) + 1 >;
[T(n, k): k in [0..n], n in [0..12]]; // _G. C. Greubel, Feb 14 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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