A161922 - OEIS

%I #8 May 01 2019 05:52:43

%S 2,6,12,14,24,26,30,48,50,54,62,56,60,96,98,102,110,126,104,108,114,

%T 122,192,194,198,206,222,254,120,200,204,210,218,230,246,384,386,390,

%U 398,414,446,510,216,224,228,236,242,252,392,396,402,410,422,438,462,494,768,770

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

%C 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.

%C 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).

%e 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.

%e The table has A160644(n) integers in row n and starts

%e 2,

%e 6,.......[2,2]->6

%e 12,14,..........[3,3]->12, [2,2,2]->14

%e 24,26,30,...........[4,4]->24, [2,3,3]->26, [2,2,2,2] ->30

%e 48,50,54,62, ....... [5,5]->48, [2,4,4]->50, [2,2,3,3]->54, [2,2,2,2,2]->62

%e 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

%e 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

%p 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:

%p 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:

%p for n from 1 to 11 do A161922(n) ; od; # _R. J. Mathar_, Sep 11 2009

%K nonn,tabf

%O 1,1

%A _Alford Arnold_, Jul 06 2009

%E Detailed description and examples and rows n >= 8 completed by _R. J. Mathar_, Sep 11 2009