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A134226
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Triangle T(n, k) = 3*n - 4 if k = n-1 otherwise k, read by rows.
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2
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1, 2, 2, 1, 5, 3, 1, 2, 8, 4, 1, 2, 3, 11, 5, 1, 2, 3, 4, 14, 6, 1, 2, 3, 4, 5, 17, 7, 1, 2, 3, 4, 5, 6, 20, 8, 1, 2, 3, 4, 5, 6, 7, 23, 9, 1, 2, 3, 4, 5, 6, 7, 8, 26, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 29, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 32, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 35, 13
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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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T(n, k) = A134082(n, k) + A002260(n, k) - I, an infinite lower triangular matrix and I = Identity matrix.
T(n, k) = 3*n - 4 if k = n-1 otherwise k.
Sum_{k=1..n} T(n, k) = A134227(n) = (n-1)*(n+6)/2 + [n=1]. (End)
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EXAMPLE
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First few rows of the triangle are:
1;
2, 2;
1, 5, 3;
1, 2, 8, 4;
1, 2, 3, 11, 5;
1, 2, 3, 4, 14, 6;
1, 2, 3, 4, 5, 17, 7;
...
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MATHEMATICA
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T[n_, k_]:= If[k==n-1, 3*n-4, k];
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 A134226(n, k): return 3*n-4 if k==n-1 else k
(Magma)
A134226:= func< n, k | k eq n-1 select 3*n-4 else k >;
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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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