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 A208482 Triangle read by rows: T(n,k) = sum of positive k-th ranks of all partitions of n. 10
 0, 1, 1, 2, 1, 1, 4, 1, 2, 1, 7, 1, 3, 2, 1, 12, 2, 5, 4, 2, 1, 18, 3, 6, 6, 4, 2, 1, 29, 6, 9, 10, 7, 4, 2, 1, 42, 9, 11, 13, 11, 7, 4, 2, 1, 63, 16, 15, 19, 17, 12, 7, 4, 2, 1, 89, 24, 18, 25, 24, 18, 12, 7, 4, 2, 1, 128, 39, 24, 36, 34, 28, 19, 12, 7, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS For the definition of the k-th rank see A208478. It appears that the sum of the k-th ranks of all partitions of n is equal to zero. It appears that reversed rows converge to A000070, the same as A208478. - Omar E. Pol, Mar 10 2012 LINKS Alois P. Heinz, Rows n = 1..44, flattened EXAMPLE For n = 4 the partitions of 4 and the four types of ranks of the partitions of 4 are ---------------------------------------------------------- Partitions    First      Second       Third      Fourth of 4          rank        rank        rank        rank ---------------------------------------------------------- 4           4-1 =  3    0-1 = -1    0-1 = -1    0-1 = -1 3+1         3-2 =  1    1-1 =  0    0-1 = -1    0-0 =  0 2+2         2-2 =  0    2-2 =  0    0-0 =  0    0-0 =  0 2+1+1       2-3 = -1    1-1 =  0    1-0 =  1    0-0 =  0 1+1+1+1     1-4 = -3    1-0 =  1    1-0 =  1    1-0 =  1 ---------------------------------------------------------- The sums of positive k-th ranks of the partitions of 4 are 4, 1, 2, 1 so row 4 lists 4, 1, 2, 1. Triangle begins: 0; 1,    1; 2,    1,  1; 4,    1,  2,  1; 7,    1,  3,  2,  1; 12,   2,  5,  4,  2,  1; 18,   3,  6,  6,  4,  2,  1; 29,   6,  9, 10,  7,  4,  2,  1; 42,   9, 11, 13, 11,  7,  4,  2,  1; 63,  16, 15, 19, 17, 12,  7,  4,  2,  1; 89,  24, 18, 25, 24, 18, 12,  7,  4,  2,  1; 128, 39, 24, 36, 34, 28, 19, 12,  7,  4,  2,  1; CROSSREFS Column 1 is A209616. Row sums give A208483. Cf. A006128, A063995, A064173, A105805, A181187, A194547, A194549, A195822, A208478. Sequence in context: A105477 A325772 A226174 * A199856 A301906 A302150 Adjacent sequences:  A208479 A208480 A208481 * A208483 A208484 A208485 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Mar 07 2012 EXTENSIONS Terms a(1)-a(22) confirmed and additional terms added by John W. Layman, Mar 10 2012 STATUS approved

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Last modified November 27 04:53 EST 2021. Contains 349346 sequences. (Running on oeis4.)