|
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|