login
A128623
Triangle read by rows: A128621 * A000012 as infinite lower triangular matrices.
3
1, 2, 2, 6, 3, 3, 8, 8, 4, 4, 15, 10, 10, 5, 5, 18, 18, 12, 12, 6, 6, 28, 21, 21, 14, 14, 7, 7, 32, 32, 24, 24, 16, 16, 8, 8, 45, 36, 36, 27, 27, 18, 18, 9, 9, 50, 50, 40, 40, 30, 30, 20, 20, 10, 10, 66, 55, 55, 44, 44, 33, 33, 22, 22, 11, 11, 72, 72, 60, 60, 48, 48, 36, 36, 24, 24, 12, 12, 91, 78, 78, 65, 65, 52, 52, 39, 39, 26, 26, 13, 13
OFFSET
1,2
FORMULA
Sum_{k=1..n} T(n, k) = A128624(n) (row sums).
T(n,k) = n*(1+floor((n-k)/2)), 1 <= k <= n. - R. J. Mathar, Jun 27 2012
From G. C. Greubel, Mar 13 2024: (Start)
T(n, k) = n*A115514(n, k).
T(n, k) = Sum_{j=k..n} A128621(n, j).
T(n, 1) = A093005(n).
T(n, 2) = A093353(n-1), n >= 2.
T(n, n) = A000027(n).
T(2*n-1, n) = A245524(n).
Sum_{k=1..n} (-1)^k*T(n, k) = (1/2)*(1-(-1)^n)*A000384(floor((n+1)/2)). (End)
EXAMPLE
First few rows of the triangle are:
1;
2, 2;
6, 3, 3;
8, 8, 4, 4;
15, 10, 10, 5, 5;
18, 18, 12, 12, 6, 6;
28, 21, 21, 14, 14, 7, 7;
...
MATHEMATICA
Table[n*Floor[(n-k+2)/2], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Mar 13 2024 *)
PROG
(Magma) [n*Floor((n-k+2)/2): k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 13 2024
(SageMath) flatten([[n*((n-k+2)//2) for k in range(1, n+1)] for n in range(1, 16)]) # G. C. Greubel, Mar 13 2024
CROSSREFS
Cf. A128624 (row sums).
Sequence in context: A338449 A163890 A298983 * A182701 A277011 A277021
KEYWORD
nonn,easy,tabl
AUTHOR
Gary W. Adamson, Mar 14 2007
EXTENSIONS
a(41) = 27 inserted and more terms from Georg Fischer, Jun 05 2023
STATUS
approved