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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.)