proposed

approved

editing

proposed

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.

proposed

editing

editing

proposed

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.

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).

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).

for n from 1 to 11 do A161922(n) ; od; # _R. J. Mathar, _, Sep 11 2009

Detailed description and examples, and rows n >= 8 completed - _by _R. J. Mathar_, Sep 11 2009

approved

editing

_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

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

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

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

approved