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A244051 Triangle read by rows in which row n lists the parts of the partitions of n into equal parts, in nonincreasing order. 0
1, 2, 1, 1, 3, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 6, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 8, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 9, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 5, 5, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n has length sigma(n) = A000203(n).

Row sums give n*d(n) = A038040(n).

Column 1 is A000027.

Both columns 2 and 3 are A032742, n > 1.

For any k > 0 and t > 0, the sequence contains exactly one run of k consecutive t's. - Rémy Sigrist, Feb 11 2019

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

Triangle begins:

  1;

  2, 1, 1;

  3, 1, 1, 1;

  4, 2, 2, 1, 1, 1, 1;

  5, 1, 1, 1, 1, 1;

  6, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1;

  7, 1, 1, 1, 1, 1, 1, 1;

  8, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1;

  9, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1;

  10, 5, 5, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;

  ...

For n = 6 the 11 partitions of 6 are [6], [3, 3], [4, 2], [2, 2, 2], [5, 1], [3, 2], [4, 1, 1], [2, 2, 1, 1], [3, 1, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]. There are only four partitions of 6 that contain equal parts so the 6th row of triangle is [6], [3, 3], [2, 2, 2], [1, 1, 1, 1, 1, 1]. The number of parts equals sigma(6) = A000203(6) = 12. The row sum is A038040(6) = 6*A000005(6) = 6*4 = 24.

PROG

(PARI) tabf(nn) = {for (n=1, nn, d = Vecrev(divisors(n)); for (i=1, #d, for (j=1, n/d[i], print1(d[i], ", ")); ); print(); ); } \\ Michel Marcus, Nov 08 2014

CROSSREFS

Cf. A000005, A000041, A000203, A032742, A038040, A237270, A237593.

Sequence in context: A167269 A105535 A182980 * A207974 A239454 A108888

Adjacent sequences:  A244048 A244049 A244050 * A244052 A244053 A244054

KEYWORD

nonn,tabf,easy

AUTHOR

Omar E. Pol, Nov 08 2014

STATUS

approved

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Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)