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 A182285 Triangle read by rows: T(n,k) = sum of all parts in the k-th zone of the last section of the set of partitions of n. 1
 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row n lists A000041(n-1) 1's together with A002865(n) n's. LINKS Table of n, a(n) for n=1..86. EXAMPLE Illustration of three arrangements of the last section of the set of partitions of 7 and the zone numbers: -------------------------------------------------------- Zone \ a) b) c) -------------------------------------------------------- 15 (7) (7) (. . . . . . 7) 14 (4+3) (4+3) (. . . 4 . . 3) 13 (5+2) (5+2) (. . . . 5 . 2) 12 (3+2+2) (3+2+2) (. . 3 . 2 . 2) 11 (1) (1) (1) 10 (1) (1) (1) 9 (1) (1) (1) 8 (1) (1) (1) 7 (1) (1) (1) 6 (1) (1) (1) 5 (1) (1) (1) 4 (1) (1) (1) 3 (1) (1) (1) 2 (1) (1) (1) 1 (1) (1) (1) . For n = 7 and k = 12 we can see that in the 12th zone of the last section of 7 the parts are 3, 2, 2, therefore T(7,12) = 3+2+2 = 7. Written as a triangle begins: 1; 1,2; 1,1,3; 1,1,1,4,4; 1,1,1,1,1,5,5; 1,1,1,1,1,1,1,6,6,6,6; 1,1,1,1,1,1,1,1,1,1,1,7,7,7,7; 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,8,8,8,8; CROSSREFS Row n has length A000041(n). Row sums give A138879. Cf. A000041, A002865, A135010, A138121, A182284, A193173. Sequence in context: A108888 A124021 A109626 * A160182 A195825 A098824 Adjacent sequences: A182282 A182283 A182284 * A182286 A182287 A182288 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Apr 23 2012 STATUS approved

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Last modified July 23 08:23 EDT 2024. Contains 374546 sequences. (Running on oeis4.)