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A231071 Number of solutions to n = +- 1^2 +- 2^2 +- 3^2 +- 4^2 +- ... +- k^2 for minimal k giving at least one solution. 4
2, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 9, 1, 3, 1, 1, 1, 2, 1, 1, 6, 1, 1, 1, 1, 1, 2, 1, 5, 1, 1, 1, 1, 4, 3, 1, 2, 1, 2, 2, 1, 2, 1, 14, 2, 1, 3, 2, 1, 2, 1, 1, 7, 1, 3, 2, 5, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This type of sequence was first studied by Andrica and Vacaretu. - Jonathan Sondow, Nov 06 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Andrica, D., Vacaretu, D., Representation theorems and almost unimodal sequences, Studia Univ. Babes-Bolyai, Mathematica, Vol. LI, 4 (2006), 23-33.

FORMULA

From Jonathan Sondow, Nov 03 2013: (Start)

a(n(n+1)(2n+1)/6) = 1 for n > 0: n(n+1)(2n+1)/6 = 1+4+9+...+n^2. See A000330.

a(n(n+1)(2n+1)/6 - 2) = 1 for n > 1: n(n+1)(2n+1)/6 - 2 = -1+4+9+...+n^2. (End)

EXAMPLE

a(8) = 3: 8 = -1-4-9-16+25-36+49 = -1-4+9+16-25-36+49 = -1+4+9-16+25+36-49.

a(9) = 2: 9 = -1-4+9+16+25-36 = 1+4+9-16-25+36.

a(10) = 1: 10 = -1+4-9+16.

MAPLE

b:= proc(n, i) option remember; (m->`if`(n>m, 0, `if`(n=m, 1,

      b(n+i^2, i-1) +b(abs(n-i^2), i-1))))((1+(3+2*i)*i)*i/6)

    end:

a:= proc(n) local k; for k while b(n, k)=0 do od; b(n, k) end:

seq(a(n), n=0..100);

CROSSREFS

Cf. A000330, A231015, A231272.

Cf. A083527, A158092 (extremal sums).

Sequence in context: A204112 A186027 A322482 * A209156 A329325 A191004

Adjacent sequences:  A231068 A231069 A231070 * A231072 A231073 A231074

KEYWORD

nonn,look

AUTHOR

Alois P. Heinz, Nov 03 2013

STATUS

approved

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Last modified June 14 09:06 EDT 2021. Contains 345018 sequences. (Running on oeis4.)