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A328371
Irregular triangle read by rows: T(n,k) is the sum of all parts of all partitions of all positive integers <= n into k consecutive parts.
2
1, 3, 6, 3, 10, 3, 15, 8, 21, 8, 6, 28, 15, 6, 36, 15, 6, 45, 24, 15, 55, 24, 15, 10, 66, 35, 15, 10, 78, 35, 27, 10, 91, 48, 27, 10, 105, 48, 27, 24, 120, 63, 42, 24, 15, 136, 63, 42, 24, 15, 153, 80, 42, 24, 15, 171, 80, 60, 42, 15, 190, 99, 60, 42, 15, 210, 99, 60, 42, 35, 231, 120, 81, 42, 35, 21
OFFSET
1,2
COMMENTS
Column k lists the partial sums of the k-th column of triangle A285891.
EXAMPLE
Triangle begins:
1;
3;
6, 3;
10, 3;
15, 8;
21, 8, 6;
28, 15, 6;
36, 15, 6;
45, 24, 15;
55, 24, 15, 10;
66, 35, 15, 10;
78, 35, 27, 10;
91, 48, 27, 10;
105, 48, 27, 24,
120, 63, 42, 24, 15;
136, 63, 42, 24, 15;
153, 80, 42, 24, 15;
171, 80, 60, 42, 15;
190, 99, 60, 42, 15;
210, 99, 60, 42, 35;
231, 120, 81, 42, 35, 21;
253, 120, 81, 64, 35, 21;
276, 143, 81, 64, 35, 21;
300, 143, 105, 64, 35, 21;
325, 168, 105, 64, 60, 21;
351, 168, 105, 90, 60, 21;
378, 195, 132, 90, 60, 48;
406, 195, 132, 90, 60, 48, 28;
...
PROG
(PARI) tt(n, k) = n*(if (k % 2, (n % k) == 0, ((n - k/2) % k) == 0)); \\ A285891
t(n, k) = sum(j=k*(k+1)/2, n, tt(j, k));
tabf(nn) = {for (n=1, nn, for (k=1, floor((sqrt(1+8*n)-1)/2), print1(t(n, k), ", "); ); print(); ); } \\ Michel Marcus, Nov 04 2019
CROSSREFS
Row sums give A285900.
Row n has length A003056(n).
Column 1 gives the nonzero terms of A000217.
Column k starts with A000217(k) in the row A000217(k).
Sequence in context: A260303 A055373 A263333 * A134440 A129529 A298263
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Nov 02 2019
STATUS
approved