A059982 Symmetric array of numeric partitions related to 1 4 9 16 ... and 1 3 4 7 13 ..., read by rows.

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

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

Table of n, a(n) for n=0..80.

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