A141659 Triangle: t(n,m)=Mod[PartitionsP[Prime[n + 1]*m + Floor[Prime[n + 1]/2] + m], Prime[n + 1]].

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

Offset

1,4

Links

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

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[%]

Prog

(PARI) T(n, k) = if (n>=k, numbpart((prime(n + 1)*k + prime(n + 1)\2 + k)) % prime(n+1)); \\ Michel Marcus, Feb 24 2023

Crossrefs

Sequence in context: A087318 A087319 A101348 * A355859 A294519 A123515

Adjacent sequences: A141656 A141657 A141658 * A141660 A141661 A141662

Keyword

nonn,tabl,uned,less

Author

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

Status

approved