A260672 Table read by rows: T(n,k) = n - A001318(k), k = 0 .. A193832(n)-1.

0, 1, 0, 2, 1, 0, 3, 2, 1, 4, 3, 2, 5, 4, 3, 0, 6, 5, 4, 1, 7, 6, 5, 2, 0, 8, 7, 6, 3, 1, 9, 8, 7, 4, 2, 10, 9, 8, 5, 3, 11, 10, 9, 6, 4, 12, 11, 10, 7, 5, 0, 13, 12, 11, 8, 6, 1, 14, 13, 12, 9, 7, 2, 15, 14, 13, 10, 8, 3, 0, 16, 15, 14, 11, 9, 4, 1, 17, 16

Offset: 0

Author

Reinhard Zumkeller, Nov 15 2015

Keywords

• nonn
• tabf
• look

Comments

Column k starts at row A001318(k); each column = A001477.

Examples

			.   0:    0
.   1:    1   0
.   2:    2   1   0
.   3:    3   2   1
.   4:    4   3   2
.   5:    5   4   3   0
.   6:    6   5   4   1
.   7:    7   6   5   2   0
.   8:    8   7   6   3   1
.   9:    9   8   7   4   2
.  10:   10   9   8   5   3
.  11:   11  10   9   6   4
.  12:   12  11  10   7   5   0
.  13:   13  12  11   8   6   1
.  14:   14  13  12   9   7   2
.  15:   15  14  13  10   8   3   0
.  16:   16  15  14  11   9   4   1
.  17:   17  16  15  12  10   5   2
.  18:   18  17  16  13  11   6   3
.  19:   19  18  17  14  12   7   4
.  20:   20  19  18  15  13   8   5  .
		

Links

• Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened
• Sylvie Corteel, Carla D. Savage, Herbert S. Wilf, Doron Zeilberger, A pentagonal number sieve, J. Combin. Theory Ser. A 82 (1998), no. 2, 186-192.
• Eric Weisstein's World of Mathematics, Pentagonal Number Theorem
• Wikipedia, Pentagonal number theorem

Crossrefs

Cf. A001318, A193832 (row lengths), A000041, A087960, A054440, A260664, A260706 (row sums).

Programs

Haskell

a260672 n k = a260672_tabf !! n !! k
a260672_row n = a260672_tabf !! n
a260672_tabf = map (takeWhile (>= 0) . flip map a001318_list . (-)) [0..]

Formula

Number of m-tuples of partitions of n that have no part in common = Sum(A087960(k)*A000041(T(n,k))^m: k = 0 .. A193832(n+1)-1), e.g. A054440 (m=2) and A260664 (m=3); see Wilf link: p. 2, (3).