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A128622
Triangle T(n, k) = A128064(unsigned) * A128174, read by rows.
2
1, 1, 2, 3, 2, 3, 3, 4, 3, 4, 5, 4, 5, 4, 5, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12
OFFSET
1,3
FORMULA
T(n, k) = abs(A128064(n,k) * A128174(n, k), as infinite lower triangular matrices.
Sum_{k=1..n} T(n, k) = A014848(n) (row sums).
From G. C. Greubel, Mar 14 2024: (Start)
T(n, k) = n - (1 - (-1)^(n+k))/2 = n - (n+k mod 2).
T(n, 1) = A109613(n+1).
T(n, n) = A000027(n).
T(2*n-1, n) = A042963(n).
T(3*n-1, n) = A016777(n+1).
T(4*n-3, n) = A047461(n).
Sum_{k=1..n} (-1)^(k-1)*T(n, k) = A319556(n).
Sum_{k=1..floor((n+1)/2)} T(n-k+1, k) = A000326(floor((n+1)/2)).
Sum_{k=1..floor((n+1)/2)} (-1)^(k-1)*T(n-k+1, k) = A123684(floor((n+1)/2)). (End)
EXAMPLE
First few rows of the triangle are:
1;
1, 2;
3, 2, 3;
3, 4, 3, 4;
5, 4, 5, 4, 5;
5, 6, 5, 6, 5, 6;
7, 6, 7, 6, 7, 6, 7;
...
MATHEMATICA
Table[n - Mod[n+k, 2], {n, 16}, {k, n}]//Flatten (* G. C. Greubel, Mar 14 2024 *)
PROG
(Magma) [n - ((n+k) mod 2): k in [1..n], n in [1..16]]; // G. C. Greubel, Mar 14 2024
(SageMath) flatten([[n - ((n+k)%2) for k in range(1, n+1)] for n in range(1, 16)]) # G. C. Greubel, Mar 14 2024
CROSSREFS
Cf. A000326 (diagonal sums), A014848 (row sums), A319556 (alternating row sums).
Sequence in context: A304331 A241834 A086389 * A026256 A079715 A030397
KEYWORD
nonn,tabl,easy
AUTHOR
Gary W. Adamson, Mar 14 2007
EXTENSIONS
More terms added by G. C. Greubel, Mar 14 2024
STATUS
approved