A141661 - OEIS

%I #10 Mar 05 2020 03:13:39

%S 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,

%T 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,

%U 13,17,0

%N 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).

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

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

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

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

%e {0},

%e {0, 0},

%e {1, 1, 0},

%e {2, 2, 0, 2},

%e {3, 0, 0, 0, 1},

%e {5, 0, 0, 7, 7, 1},

%e {7, 0, 0, 0, 8, 9, 1},

%e {11, 3, 12, 9, 0, 6, 11, 11},

%e {0, 10, 0, 1, 0, 8, 5, 10, 11},

%e {5, 5, 1, 13, 8, 8, 5, 0, 5, 3},

%e {11, 5, 17, 15, 9, 6, 3, 8, 13, 17, 0}

%t << DiscreteMath`Combinatorica`;

%t << DiscreteMath`IntegerPartitions`;

%t T[n_, m_] = Mod[PartitionsP[(2*n - 1)*m + Floor[(2*n - 1)/2] + m], (2*n - 1)];

%t Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl,less,uned

%O 1,7

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 05 2008