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A134231
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Triangle T(n, k) = n -k +1 with T(n, n-1) = 2*n-1 and T(n, n) = 1, read by rows.
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1
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1, 3, 1, 3, 5, 1, 4, 3, 7, 1, 5, 4, 3, 9, 1, 6, 5, 4, 3, 11, 1, 7, 6, 5, 4, 3, 13, 1, 8, 7, 6, 5, 4, 3, 15, 1, 9, 8, 7, 6, 5, 4, 3, 17, 1, 10, 9, 8, 7, 6, 5, 4, 3, 19, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 21, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 23, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 25, 1
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OFFSET
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1,2
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LINKS
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G. C. Greubel, Rows n = 1..50 of the triangle, flattened
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FORMULA
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T(n, k) = A004736(n, k) + A134081(n, k) - I, an infinite lower triangular matrix, where I = Identity matrix.
From G. C. Greubel, Feb 17 2021: (Start)
T(n, k) = n - k + 1 with T(n, n-1) = 2*n - 1 and T(n, n) = 1.
Sum_{k=1..n} T(n, k) = (n-1)*(n+6)/2 + [n=1] = A134227(n). (End)
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EXAMPLE
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First few rows of the triangle are:
1;
3, 1;
3, 5, 1;
4, 3, 7, 1;
5, 4, 3, 9, 1;
6, 5, 4, 3, 11, 1;
7, 6, 5, 4, 3, 13, 1;
...
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MATHEMATICA
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T[n_, k_]:= If[k==n, 1, If[k==n-1, 2*n-1, n-k+1]];
Table[T[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Feb 17 2021 *)
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PROG
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(Sage)
def A134231(n, k): return 1 if k==n else 2*n-1 if k==n-1 else n-k+1
flatten([[A134231(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Feb 17 2021
(Magma)
A134231:= func< n, k | k eq n select 1 else k eq n-1 select 2*n-1 else n-k+1 >;
[A134231(n, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Feb 17 2021
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CROSSREFS
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Cf. A004736, A134081, A134227.
Sequence in context: A210952 A208523 A209572 * A225598 A126637 A110091
Adjacent sequences: A134228 A134229 A134230 * A134232 A134233 A134234
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Oct 14 2007
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EXTENSIONS
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More terms and title changed by G. C. Greubel, Feb 17 2021
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STATUS
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approved
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