A004441 Numbers that are not the sum of 4 distinct nonzero squares.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 52, 53, 55, 56, 58, 59, 60, 61, 64, 67, 68

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

It has been shown that 157 is the last odd number in this sequence. Beyond 157, the terms grow exponentially. - T. D. Noe, Apr 07 2007

Taking a(86) to a(120) as initial terms, A004441(n) satisfies the 35th-order recurrence relation u(n) = 4*u(n-35). - Ant King, Aug 13 2010

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000 (using A004195 and A004196)
• Paul T. Bateman, Adolf J. Hildebrand and George B. Purdy, Sums of distinct squares, Acta Arith. 67 (1994), 349-380.
• H. D. Nguyen and D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013. [Mentions this sequence.]
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4).
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A004195, A004196, A004433 (complement).

Programs

Mathematica

data1=Reduce[w^2+x^2+y^2+z^2==# && 00,0,k],{k,1,Length[data2]}],0] (* Ant King, Aug 13 2010 *)