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URL: https://oeis.org/A342797

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A342797
Irregular triangle read by rows: T(n, k) is the k-th antidiagonal sum of the n X n matrices defined in A069480 and A078475.
0
1, 1, 5, 4, 1, 5, 15, 15, 9, 1, 5, 15, 34, 36, 29, 16, 1, 5, 15, 34, 65, 70, 63, 47, 25, 1, 5, 15, 34, 65, 111, 120, 114, 96, 69, 36, 1, 5, 15, 34, 65, 111, 175, 189, 185, 166, 135, 95, 49, 1, 5, 15, 34, 65, 111, 175, 260, 280, 279, 260, 226, 180, 125, 64
OFFSET
1,3
FORMULA
T(n, k) = A006003(k) for 1 <= k <= n.
T(n, k) = (k^3 + 2*n - 6*k^2*n - 4*n^3 + k*(10*n^2 - 1))/2 for n < k <= 2*n - 1.
T(n, 2*n-1) = A000290(n).
EXAMPLE
The triangle T(n, k) begins:
1
1 5 4
1 5 15 15 9
1 5 15 34 36 29 16
1 5 15 34 65 70 63 47 25
...
MATHEMATICA
T[n_, k_]:=If[k<=n, (k+k^3)/2, (k^3+2n-6k^2n-4n^3+k(10n^2-1))/2]; Flatten[Table[T[n, k], {n, 8}, {k, 2n-1}]]
CROSSREFS
Cf. A000290 (diagonal), A006003, A037270 (row sums), A060747 (row length), A069480, A078475.
Sequence in context: A113011 A028875 A130815 * A084129 A011503 A296498
KEYWORD
nonn,tabf
AUTHOR
Stefano Spezia, Apr 25 2021
STATUS
approved