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A161922 Table with the mapped A125106(p) in row n where p runs through the partitions counted by A160644(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=1..58.

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

Sequence in context: A190503 A320149 A140760 * A027863 A261978 A236264

Adjacent sequences:  A161919 A161920 A161921 * A161923 A161924 A161925

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

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Last modified June 7 03:27 EDT 2020. Contains 334836 sequences. (Running on oeis4.)