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

Author

Alford Arnold, Mar 06 2001

Keywords

• easy
• nonn
• tabf

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.

Examples

			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
		

References

• Kass, Moody, Patera and Slansky (1990), Affine Lie Algebras, Weight Multiplicities and Branching Rules. University of California Press. Vol. I, page 108.

Crossrefs

A000041, A000290, A029552 and A049597.