

A141659


A triangular sequence of partitions based on ideas of congruences in Primes: t(n,m)=Mod[PartitionsP[Prime[n + 1]*m + Floor[Prime[n + 1]/2] + m], Prime[n + 1]].


0



1, 1, 1, 2, 2, 0, 3, 0, 0, 0, 7, 0, 0, 0, 8, 11, 3, 12, 9, 0, 6, 5, 5, 1, 13, 8, 8, 5, 11, 5, 17, 15, 9, 6, 3, 8, 10, 2, 2, 1, 14, 12, 6, 12, 9, 19, 7, 15, 26, 8, 14, 3, 12, 10, 1, 21, 10, 20, 12, 10, 9, 15, 28, 26, 21, 6
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OFFSET

1,4


COMMENTS

Row sums are:
{1, 2, 4, 3, 15, 41, 45, 74, 68, 115, 178}.


REFERENCES

Weisstein, Eric W. "Partition Function P Congruences." http://mathworld.wolfram.com/PartitionFunctionPCongruences.html


LINKS

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


FORMULA

t(n,m)= Mod[PartitionsP[Prime[n + 1]*m + Floor[Prime[n + 1]/2] + m], Prime[n + 1]].


EXAMPLE

{1},
{1, 1},
{2, 2, 0},
{3, 0, 0, 0},
{7, 0, 0, 0, 8},
{11, 3, 12, 9, 0, 6},
{5, 5, 1, 13, 8, 8, 5},
{11, 5, 17, 15, 9, 6, 3, 8},
{10, 2, 2, 1, 14, 12, 6, 12, 9},
{19, 7, 15, 26, 8, 14, 3, 12, 10, 1},
{21, 10, 20, 12, 10, 9, 15, 28, 26, 21, 6}


MATHEMATICA

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


CROSSREFS

Sequence in context: A087318 A087319 A101348 * A294519 A123515 A058648
Adjacent sequences: A141656 A141657 A141658 * A141660 A141661 A141662


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 04 2008


STATUS

approved



