A180149 Integers with precisely two partitions into sums of four squares of nonnegative numbers.

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

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(n-8).

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. 476-481.

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 5*2^N, 11*2^N and {1,3,30,46}*4^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 !! (n-1)
a180149_list = filter ((== 2) . a002635) [0..]
-- Reinhard Zumkeller, Jul 13 2014

Crossrefs

Cf. A002635, A006431, A245022.

Sequence in context: A352323 A175308 A244533 * A155879 A172192 A243194

Adjacent sequences: A180146 A180147 A180148 * A180150 A180151 A180152

Keyword

easy,nonn

Author

Ant King, Aug 17 2010

Status

approved