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A178067
Triangle read by rows: T(n,k) = (n^2 + k)*(n - k + 1)/2.
2
1, 5, 3, 15, 11, 6, 34, 27, 19, 10, 65, 54, 42, 29, 15, 111, 95, 78, 60, 41, 21, 175, 153, 130, 106, 81, 55, 28, 260, 231, 201, 170, 138, 105, 71, 36, 369, 332, 294, 255, 215, 174, 132, 89, 45, 505, 459, 412, 364, 315, 265, 214, 162, 109, 55, 671, 615, 558, 500, 441, 381, 320, 258, 195, 131, 66
OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
FORMULA
As infinite lower triangular matrices, A000027 * A000012 (the all 1's triangle).
EXAMPLE
First few rows of the triangle:
1;
5, 3;
15, 11, 6;
34, 27, 19, 10;
65, 54, 42, 29, 15;
111, 95, 78, 60, 41, 21;
175, 153, 130, 106, 81, 55, 28;
260, 231, 201, 170, 138, 105, 71, 36;
369, 332, 294, 255, 215, 174, 132, 89, 45;
505, 459, 412, 364, 315, 265, 214, 162, 109, 55;
671, 615, 558, 500, 441, 381, 320, 258, 195, 131, 66;
...
Example: Row 3 = (15, 11 6) since row 3 of A000027 as a triangle = (4, 5, 6); then taking partial sums from the right.
CROSSREFS
Column 1 is A006003.
Row sums are A132117.
Main diagonal is A000217.
Sequence in context: A162813 A146934 A213762 * A213548 A246204 A185733
KEYWORD
nonn,tabl,easy
AUTHOR
Gary W. Adamson, May 18 2010
EXTENSIONS
Name changed and terms a(37) and beyond from Andrew Howroyd, Apr 17 2021
STATUS
approved