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.
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
KEYWORD
easy,nonn
AUTHOR
Ant King, Aug 17 2010
STATUS
approved