1,1

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).

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

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

Sequence in context: A057895 A111369 A140760 this_sequence A027863 A152301 A152389

Adjacent sequences: A161919 A161920 A161921 this_sequence A161923 A161924 A161925

nonn,tabf

Alford Arnold (Alford1940(AT)aol.com), Jul 06 2009

Detailed description and examples, rows n>=8 completed - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2009