A330377 - OEIS

A330377

Irregular triangle read by rows: T(n,k) is the sum of all parts of all partitions of n with Durfee square of size k, (n >= 1; 1 <= k <= floor(sqrt(n))).

1, 4, 9, 16, 4, 25, 10, 36, 30, 49, 56, 64, 112, 81, 180, 9, 100, 300, 20, 121, 440, 55, 144, 660, 120, 169, 910, 234, 196, 1274, 420, 225, 1680, 735, 256, 2240, 1184, 16, 289, 2856, 1870, 34, 324, 3672, 2844, 90, 361, 4560, 4199, 190, 400, 5700, 6040, 400, 441, 6930, 8547, 714, 484, 8470, 11792, 1298

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..62.

FORMULA

T(n,k) = n*A115994(n,k).

EXAMPLE

Triangle begins:

16, 4;

25, 10;

36, 30;

49, 56;

64, 112;

81, 180, 9;

100, 300, 20;

121, 440, 55;

144, 660, 120;

169, 910, 234;

196, 1274, 420;

225, 1680, 735;

256, 2240, 1184, 16;

289, 2856, 1870, 34;

324, 3672, 2844, 90;

361, 4560, 4199, 190;

400, 5700, 6040, 400;

441, 6930, 8547, 714;

484, 8470, 11792, 1298;

...

CROSSREFS

Row sums give A066186.

Row lengths give A000196, n >= 1.

Column 1 gives A000290, n >= 1.

Column k starts at row k^2 with k^2.

Cf. A115994.

Sequence in context: A120866 A070443 A279403 * A070643 A070442 A086957

Adjacent sequences: A330374 A330375 A330376 * A330378 A330379 A330380

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Dec 22 2019

STATUS

approved