[go: up one dir, main page]

login
A097563
Least integer that can be written as a sum of zero or more distinct squares in exactly n ways, or -1 if no such number exists.
17
2, 0, 25, 50, 65, 94, 90, 110, 155, 126, 191, 170, 186, 174, 190, 211, 195, 226, 210, 231, 234, 235, 332, 255, 283, 259, 274, 275, 270, 323, 310, 286, 306, 299, 330, 381, 295, 347, 334, 319, 315, 331, 405, 339, 335, 364, 359, 351, 367, 387, 371, 370, 404, 438
OFFSET
0,1
COMMENTS
a(n) = -1 for almost all n. Conjecture: for n > 34189857569982621, this sequence is the integers > 37163, in order, interspersed with -1s. - Charles R Greathouse IV, Sep 04 2015
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
EXAMPLE
a(4) = 65 because we can write 65 as a sum of distinct squares in four ways: 65 = 8^2 + 1^2 = 7^2 + 4^2 = 6^2 + 5^2 + 2^2 = 6^2 + 4^2 + 3^2 + 2^2 and we cannot do this with any smaller integer.
a(0) = 2 because we cannot write 2 as a sum of distinct squares and it is the smallest number with this property.
MAPLE
gf := product(1+x^F(k), k=1..31); ser := series(gf, x=0, 1001); S := [seq(coeff(ser, x^(1*i)), i=1..1000)]; A := proc(i); x := 0; for j from 1 to nops(a) while x = 0 do > if a[j] = i then x := 1; fi; od; j-1; end; seq(A(n), n=1..67);
CROSSREFS
First occurrence of n in A033461; see also A001422 (0 ways) and A003995 (1 or more ways).
Sequence in context: A308506 A255162 A359006 * A360643 A158045 A157304
KEYWORD
easy,sign
AUTHOR
Isabel C. Lugo (izzycat(AT)gmail.com), Aug 27 2004
EXTENSIONS
Edited by Ray Chandler, Sep 01 2004
STATUS
approved