This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A225598 Triangle read by rows: T(n,k) = sum of all parts of all regions of the set of partitions of n whose largest part is k. 2
 1, 1, 3, 1, 3, 5, 1, 5, 5, 9, 1, 5, 8, 9, 12, 1, 7, 11, 15, 12, 20, 1, 7, 14, 19, 19, 20, 25, 1, 9, 17, 29, 24, 33, 25, 38, 1, 9, 23, 33, 36, 42, 39, 38, 49, 1, 11, 26, 47, 46, 61, 49, 61, 49, 69, 1, 11, 32, 55, 63, 76, 70, 76, 76, 69, 87, 1, 13, 38, 73, 78, 110, 87, 111, 95, 108, 87, 123 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For the definition of region see A206437. T(n,k) is also the sum of all parts that end in the k-th column of the diagram of regions of the set of partitions of n (see Example section). LINKS EXAMPLE For n = 5 and k = 3 the set of partitions of 5 contains two regions whose largest part is 3, they are third region which contains three parts [3, 1, 1] and the sixth region which contains only one part [3]. Therefore the sum of all parts is 3 + 1 + 1 + 3 = 8, so T(5,3) = 8. . .    Diagram    Illustration of parts ending in column k: .    for n=5      k=1   k=2     k=3       k=4        k=5 .   _ _ _ _ _                                  _ _ _ _ _ .  |_ _ _    |                _ _ _           |_ _ _ _ _| .  |_ _ _|_  |               |_ _ _|  _ _ _ _       |_ _| .  |_ _    | |          _ _          |_ _ _ _|        |_| .  |_ _|_  | |         |_ _|  _ _ _      |_ _|        |_| .  |_ _  | | |          _ _  |_ _ _|       |_|        |_| .  |_  | | | |      _  |_ _|     |_|       |_|        |_| .  |_|_|_|_|_|     |_|   |_|     |_|       |_|        |_| . k = 1 2 3 4 5 . The 5th row lists:  1     5       8         9         12 . Triangle begins: 1; 1,  3; 1,  3,  5; 1,  5,  5,  9; 1,  5,  8,  9, 12; 1,  7, 11, 15, 12,  20; 1,  7, 14, 19, 19,  20, 25; 1,  9, 17, 29, 24,  33, 25,  38; 1,  9, 23, 33, 36,  42, 39,  38, 49; 1, 11, 26, 47, 46,  61, 49,  61, 49,  69; 1, 11, 32, 55, 63,  76, 70,  76, 76,  69, 87; 1, 13, 38, 73, 78, 110, 87, 111, 95, 108, 87, 123; CROSSREFS Column 1 is A000012. Column 2 are the numbers >= 3 of A109613. Row sums give A066186. Right border gives A046746. Second right border gives A046746. Cf. A000041, A066186, A135010, A141285, A186114, A186412, A187219, A194446, A206437, A207779, A211978, A225597, A225600, A225610. Sequence in context: A208523 A209572 A134231 * A126637 A110091 A263051 Adjacent sequences:  A225595 A225596 A225597 * A225599 A225600 A225601 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Aug 02 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 25 12:01 EDT 2019. Contains 324352 sequences. (Running on oeis4.)