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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 (list; graph; refs; listen; history; text; internal format)
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)=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

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)