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A257058 Numbers k such that (# squares) > (# nonsquares) in the quarter-squares representation of k. 3
0, 1, 4, 5, 9, 10, 16, 17, 19, 25, 26, 28, 29, 35, 36, 37, 39, 40, 41, 47, 49, 50, 52, 53, 54, 61, 64, 65, 67, 68, 69, 71, 77, 81, 82, 84, 85, 86, 88, 95, 100, 101, 103, 104, 105, 107, 109, 115, 120, 121, 122, 124, 125, 126, 128, 130, 131, 137, 142, 144, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Every positive integer is a sum of at most four distinct quarter squares; see A257019.   The sequences A257056, A257057, A257058 partition the nonnegative integers.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

Quarter-square representations:

r(0) = 0, so a(1) = 0

r(1) = 1, so a(2) = 1

r(2) = 2

r(3) = 2 + 1

r(4) = 4, so a(3) = 4

MATHEMATICA

z = 400; b[n_] := Floor[(n + 1)^2/4]; bb = Table[b[n], {n, 0, 100}];

s[n_] := Table[b[n], {k, b[n + 1] - b[n]}];

h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];

g = h[100]; r[0] = {0};

r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];

u = Table[Length[r[n]], {n, 0, z}]  (* A257023 *)

v = Table[Length[Intersection[r[n], Table[n^2, {n, 0, 1000}]]], {n, 0, z}]  (* A257024 *)

-1 + Select[Range[0, z], 2 v[[#]] < u[[#]] &]   (* A257056 *)

-1 + Select[Range[0, z], 2 v[[#]] == u[[#]] &]  (* A257057 *)

-1 + Select[Range[0, z], 2 v[[#]] > u[[#]] &]   (* A257058 *)

CROSSREFS

Cf. A257019, A000290, A257056, A257057.

Sequence in context: A191888 A050036 A059582 * A189889 A329451 A308578

Adjacent sequences:  A257055 A257056 A257057 * A257059 A257060 A257061

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 15 2015

STATUS

approved

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)