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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.

%I A059982 #6 Mar 31 2012 13:23:36
%S A059982 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,
%T A059982 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,
%U A059982 56,77,56,22,3,5,30,77,101,77,30,5,7,42,101,135,101,42,7,11,56,135,176
%N A059982 Symmetric array of numeric partitions related to 1 4 9 16 ... and 1 3 4 7 13 ..., read by rows.
%C A059982 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.
%D A059982 Kass, Moody, Patera and Slansky (1990), Affine Lie Algebras, Weight Multiplicities and Branching Rules. University of California Press. Vol. I, page 108.
%e A059982 The array begins:
%e A059982 ........................1
%e A059982 ................1.......1.......1
%e A059982 ................1.......2.......1
%e A059982 ................2.......3.......2
%e A059982 ........1.......3.......5.......3.......1
%e A059982 ........1.......5.......7.......5.......1
%e A059982 ........2.......7.......11......7.......2
%e A059982 ........3.......11......15......11......3
%e A059982 ........5.......15......22......15......5
%e A059982 1.......7.......22......30......22......7.......1
%e A059982 1.......11......30......42......30......11......1
%e A059982 2.......15......42......56......42......15......2
%e A059982 3.......22......56......77......56......22......3
%e A059982 5.......30......77......101.....77......30......5
%Y A059982 A000041, A000290, A029552 and A049597.
%K A059982 easy,nonn,tabf
%O A059982 0,6
%A A059982 _Alford Arnold_, Mar 06 2001