

A141661


Ramanujan Partition odd congruences as a triangular sequence: t(n,m)=Mod[PartitionsP[(2*n  1)*m + Floor[(2*n  1)/2] + m], (2*n  1)].


0



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
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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 301302


LINKS

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


FORMULA

t(n,m)=Mod[PartitionsP[(2*n  1)*m + Floor[(2*n  1)/2] + m], (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: A236306 A153239 A229502 * A278521 A195910 A240590
Adjacent sequences: A141658 A141659 A141660 * A141662 A141663 A141664


KEYWORD

nonn,uned


AUTHOR

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


STATUS

approved



