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 A194812 Square array read by antidiagonals: T(n,k) = number of parts of size k in the last section of the set of partitions of n. 24
 1, 1, 0, 2, 1, 0, 3, 0, 0, 0, 5, 2, 1, 0, 0, 7, 1, 0, 0, 0, 0, 11, 4, 1, 1, 0, 0, 0, 15, 3, 2, 0, 0, 0, 0, 0, 22, 8, 2, 1, 1, 0, 0, 0, 0, 30, 7, 3, 1, 0, 0, 0, 0, 0, 0, 42, 15, 6, 3, 1, 1, 0, 0, 0, 0, 0, 56, 15, 6, 2, 1, 0, 0, 0, 0, 0, 0, 0, 77, 27, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS It appears that in the column k, starting in row n, the sum of k successive terms is equal to A000041(n-1). LINKS FORMULA It appears that A000041(n) = Sum_{j=1..k) T(n+j,k), n >= 0, k >= 1. EXAMPLE Array begins: .  1,  0,  0,  0, 0, 0, 0, 0, 0, 0, 0, 0,... .  1,  1,  0,  0, 0, 0, 0, 0, 0, 0, 0, 0,... .  2,  0,  1,  0, 0, 0, 0, 0, 0, 0, 0, 0,... .  3,  2,  0,  1, 0, 0, 0, 0, 0, 0, 0, 0,... .  5,  1,  1,  0, 1, 0, 0, 0, 0, 0, 0, 0,... .  7,  4,  2,  1, 0, 1, 0, 0, 0, 0, 0, 0,... . 11,  3,  2,  1, 1, 0, 1, 0, 0, 0, 0, 0,... . 15,  8,  3,  3, 1, 1, 0, 1, 0, 0, 0, 0,... . 22,  7,  6,  2, 2, 1, 1, 0, 1, 0, 0, 0,... . 30, 15,  6,  5, 3, 2, 1, 1, 0, 1, 0, 0,... . 42, 15, 10,  5, 4, 2, 2, 1, 1, 0, 1, 0,... . 56, 27, 14, 10, 5, 5, 2, 2, 1, 1, 0, 1,... ... For n = 7, from the conjecture we have that p(n-1) = p(6) = 11 = 3+8 = 2+3+6 = 1+3+2+5 = 1+1+2+3+4 = 0+1+1+2+2+5, etc. where p(n) = A000041(n). CROSSREFS Columns 1-4: A000041, A182712, A182713, A182714. Main triangle: A182703. Cf. A066633, A135010, A138121, A138137. Sequence in context: A307772 A225203 A136255 * A305320 A159813 A157409 Adjacent sequences:  A194809 A194810 A194811 * A194813 A194814 A194815 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Feb 04 2012 STATUS approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)