A128177 - OEIS

%I #18 Mar 23 2024 22:13:45

%S 1,2,1,4,2,1,6,4,2,1,9,6,4,2,1,12,9,6,4,2,1,16,12,9,6,4,2,1,20,16,12,

%T 9,6,4,2,1,25,20,16,12,9,6,4,2,1,30,25,20,16,12,9,6,4,2,1,36,30,25,20,

%U 16,12,9,6,4,2,1,42,36,30,25,20,16,12,9,6,4,2,1

%N A128174 * A004736 as infinite lower triangular matrices.

%C n-th row has n nonzero terms of A002620: (1, 2, 4, 6, 9, 12, 16, ...) in reverse.

%C Row sums = A002623: (1, 3, 7, 13, 22, 34, 50, ...).

%F From _Ridouane Oudra_, Mar 23 2024: (Start)

%F T(n, k) = A002620(n-k+2), with 1 <= k <= n;

%F T(n, k) = floor((n-k+2)^2/4);

%F T(n, k) = (1/2)*floor((n-k+2)^2/2);

%F T(n, k) = (1/8)*(2*(n-k+2)^2 + (-1)^(n-k) - 1). (End)

%e First few rows of the triangle:

%e    1;

%e    2, 1;

%e    4, 2, 1;

%e    6, 4, 2, 1;

%e    9, 6, 4, 2, 1;

%e   12, 9, 6, 4, 2, 1;

%e   ...

%p seq(seq(floor((n-k+2)^2/4), k=1..n), n=1..20); # _Ridouane Oudra_, Mar 23 2024

%o (PARI) lista(nn) = {t128174 = matrix(nn, nn, n, k, (k<=n)*(1+(-1)^(n-k))/2); t004736 = matrix(nn, nn, n, k, (k<=n)*(n - k + 1)); t128177 = t128174*t004736; for (n = 1, nn, for (k = 1, n, print1(t128177[n, k], ", ");););} \\ _Michel Marcus_, Feb 11 2014

%Y Cf. A128174, A004736, A002623, A002620.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Feb 17 2007

%E Partially edited and more terms from _Michel Marcus_, Feb 11 2014