A161922 Table with the mapped A125106(p) in row n where p runs through the partitions counted by A160644(n).

2, 6, 12, 14, 24, 26, 30, 48, 50, 54, 62, 56, 60, 96, 98, 102, 110, 126, 104, 108, 114, 122, 192, 194, 198, 206, 222, 254, 120, 200, 204, 210, 218, 230, 246, 384, 386, 390, 398, 414, 446, 510, 216, 224, 228, 236, 242, 252, 392, 396, 402, 410, 422, 438, 462, 494, 768, 770

Offset: 1

Author

Alford Arnold, Jul 06 2009

Keywords

• nonn
• tabf

Comments

A160644(n) with n > 0 counts the partitions of 2n such that all parts are > 1 and the largest part occurs more than once. If n=7, these are 10 partitions of 14: 2^7 = (2^4;3^2) = (2^1;3^4) = (2^3;4^2) = (3^2;4^2) = (2^1;4^3) = (2^2;5^2) = (4^1;5^2) = (2^1;6^2) = 7^2, for example.

For each of these admitted partitions p of 2n, p is mapped to a binary and the decimal rep. of this binary is added to row n of this table here, sorting the row according to the natural order of integers (not according to any property of partitions).

Examples

			The partition 4+4+4+4 = 16 and maps to 120 = 64 + 32 + 16 + 8 as described in A125106, so 120 is in the 8th row.
The table has A160644(n) integers in row n and starts
2,
6,.......[2,2]->6
12,14,..........[3,3]->12, [2,2,2]->14
24,26,30,...........[4,4]->24, [2,3,3]->26, [2,2,2,2] ->30
48,50,54,62, ....... [5,5]->48, [2,4,4]->50, [2,2,3,3]->54, [2,2,2,2,2]->62
56,60,96,98,102,110,126,.....[4,4,4]->56, [3,3,3,3]->60, [6,6]->96, [2,5,5]->98, [2,2,4,4]->102, [2,2,2,3,3]->110
104,108,114,122,192,194,198,206,222,254,...[4,5,5]->104, [3,3,4,4]->108, [2,4,4,4]->114, [2,3,3,3,3]->122
		

Programs

Maple

A125106m := proc(par) local c,dgs,p ; c := 1 ; dgs := [] ; for p in par do if p = c then dgs := [op(dgs),1] ; else dgs := [op(dgs),seq(0,j=1..p-c),1] ; fi; c := p ; od: add(op(i,dgs) *2^(i-1), i=1..nops(dgs)) ; end:
A161922 := proc(n) r := {} ; prts := combinat[partition](2*n) ; for p in prts do convert(p,set) intersect {1}; if % = {} then if nops(p) < 2 then ; elif op(-1,p) = op(-2,p) then r := r union {A125106m(p)} ; fi; fi; od: sort(r) ; end:
for n from 1 to 11 do A161922(n) ; od; # R. J. Mathar, Sep 11 2009

Extensions

Detailed description and examples and rows n >= 8 completed by R. J. Mathar, Sep 11 2009