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 A059982 Symmetric array of numeric partitions related to 1 4 9 16 ... and 1 3 4 7 13 ..., read by rows. 0
 1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 5, 3, 1, 1, 5, 7, 5, 1, 2, 7, 11, 7, 2, 3, 11, 15, 11, 3, 5, 15, 22, 15, 5, 1, 7, 22, 30, 22, 7, 1, 1, 11, 30, 42, 30, 11, 1, 2, 15, 42, 56, 42, 15, 2, 3, 22, 56, 77, 56, 22, 3, 5, 30, 77, 101, 77, 30, 5, 7, 42, 101, 135, 101, 42, 7, 11, 56, 135, 176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Begin with row zero and generate a column of values using the sequence of numeric partitions (A000041). At rows 1 4 9 16 25 ... A000290, generate two new columns one each to the left and right of existing columns. Note that the row sums appear to be A029552. REFERENCES Kass, Moody, Patera and Slansky (1990), Affine Lie Algebras, Weight Multiplicities and Branching Rules. University of California Press. Vol. I, page 108. LINKS EXAMPLE The array begins: ........................1 ................1.......1.......1 ................1.......2.......1 ................2.......3.......2 ........1.......3.......5.......3.......1 ........1.......5.......7.......5.......1 ........2.......7.......11......7.......2 ........3.......11......15......11......3 ........5.......15......22......15......5 1.......7.......22......30......22......7.......1 1.......11......30......42......30......11......1 2.......15......42......56......42......15......2 3.......22......56......77......56......22......3 5.......30......77......101.....77......30......5 CROSSREFS A000041, A000290, A029552 and A049597. Sequence in context: A111944 A109814 A133088 * A187801 A134388 A055095 Adjacent sequences:  A059979 A059980 A059981 * A059983 A059984 A059985 KEYWORD easy,nonn,tabf AUTHOR Alford Arnold, Mar 06 2001 STATUS approved

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Last modified November 18 01:20 EST 2018. Contains 317279 sequences. (Running on oeis4.)