A260672 - OEIS

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

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OFFSET

0,4

COMMENTS

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

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

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).

EXAMPLE

. 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 .

PROG

(Haskell)

a260672 n k = a260672_tabf !! n !! k

a260672_row n = a260672_tabf !! n

a260672_tabf = map (takeWhile (>= 0) . flip map a001318_list . (-)) [0..]

CROSSREFS

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

Sequence in context: A257962 A176095 A295508 * A063942 A263405 A106384

Adjacent sequences: A260669 A260670 A260671 * A260673 A260674 A260675

KEYWORD

nonn,tabf,look

AUTHOR

Reinhard Zumkeller, Nov 15 2015

STATUS

approved