A141661 Ramanujan Partition odd congruences as a triangular sequence: t(n,m) = PartitionsP((2*n - 1)*m + floor((2*n - 1)/2) + m) mod (2*n - 1).

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

Offset

1,7

Comments

Row sums are {0, 0, 2, 6, 4, 20, 25, 63, 45, 53, 104}.

This triangle sequence shows one or more congruence at each n level.

References

R. Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan, 1991, pages 301-302.

Links

Table of n, a(n) for n=1..66.

Formula

t(n,m) = PartitionsP((2*n - 1)*m + floor((2*n - 1)/2) + m) mod (2*n - 1).

Example

{0},
{0, 0},
{1, 1, 0},
{2, 2, 0, 2},
{3, 0, 0, 0, 1},
{5, 0, 0, 7, 7, 1},
{7, 0, 0, 0, 8, 9, 1},
{11, 3, 12, 9, 0, 6, 11, 11},
{0, 10, 0, 1, 0, 8, 5, 10, 11},
{5, 5, 1, 13, 8, 8, 5, 0, 5, 3},
{11, 5, 17, 15, 9, 6, 3, 8, 13, 17, 0}

Mathematica

<< DiscreteMath`Combinatorica`;
<< DiscreteMath`IntegerPartitions`;
T[n_, m_] = Mod[PartitionsP[(2*n - 1)*m + Floor[(2*n - 1)/2] + m], (2*n - 1)];
Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A153239 A229502 A356359 * A278521 A195910 A240590

Adjacent sequences: A141658 A141659 A141660 * A141662 A141663 A141664

Keyword

nonn,tabl,less,uned

Author

Roger L. Bagula and Gary W. Adamson, Sep 05 2008

Status

approved