OFFSET
1,1
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).
EXAMPLE
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
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
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alford Arnold, Jul 06 2009
EXTENSIONS
Detailed description and examples and rows n >= 8 completed by R. J. Mathar, Sep 11 2009
STATUS
approved