A128177 A128174 * A004736 as infinite lower triangular matrices.

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

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..78.

Formula

From Ridouane Oudra, Mar 23 2024: (Start)

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

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

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

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

Example

First few rows of the triangle:
   1;
   2, 1;
   4, 2, 1;
   6, 4, 2, 1;
   9, 6, 4, 2, 1;
  12, 9, 6, 4, 2, 1;
  ...

Maple

seq(seq(floor((n-k+2)^2/4), k=1..n), n=1..20); # Ridouane Oudra, Mar 23 2024

Prog

(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

Crossrefs

Cf. A128174, A004736, A002623, A002620.

Sequence in context: A365901 A325309 A211956 * A087738 A133113 A124840

Adjacent sequences: A128174 A128175 A128176 * A128178 A128179 A128180

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 17 2007

Extensions

Partially edited and more terms from Michel Marcus, Feb 11 2014

Status

approved