

A180149


Integers with precisely two partitions into sums of four squares of nonnegative numbers.


11



4, 9, 10, 12, 13, 16, 17, 19, 20, 21, 22, 29, 30, 31, 35, 39, 40, 44, 46, 47, 48, 64, 71, 80, 88, 120, 160, 176, 184, 192, 256, 320, 352, 480, 640, 704, 736, 768, 1024, 1280, 1408, 1920, 2560, 2816, 2944, 3072, 4096, 5120, 5632, 7680
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OFFSET

1,1


COMMENTS

The largest odd member of this sequence is 71, and from a(32)=320 onwards the terms satisfy the eighth order recurrence relation a(n)=4a(n8).
A002635(a(n)) = 2.  Reinhard Zumkeller, Jul 13 2014


LINKS

Robert Price, Table of n, a(n) for n = 1..65
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No.8, October 1948, pp. 476481.
Index entries for sequences related to sums of squares


FORMULA

The members of this sequence are {9, 13, 17, 19, 21, 29, 30, 31, 35, 39, 46, 47, 71} together with all integers of the form 5x2^N, 11x2^N and {1,3,30,46}x4^N where N>0 (which includes a necessary correction to Lehmer's result).


EXAMPLE

As the fifth integer which has precisely two partitions into sums of four squares of nonnegative numbers is 13, then a(5)=13.


MATHEMATICA

Select[Range[10000], Length[PowersRepresentations[ #, 4, 2]]==2&]


PROG

(Haskell)
a180149 n = a180149_list !! (n1)
a180149_list = filter ((== 2) . a002635) [0..]
 Reinhard Zumkeller, Jul 13 2014


CROSSREFS

Cf. A002635, A006431, A245022.
Sequence in context: A125726 A175308 A244533 * A155879 A172192 A243194
Adjacent sequences: A180146 A180147 A180148 * A180150 A180151 A180152


KEYWORD

easy,nonn


AUTHOR

Ant King, Aug 17 2010


STATUS

approved



