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 A257056 Numbers k such that (# squares) < (# nonsquares) in the quarter-squares representation of k. 3
 2, 6, 8, 12, 14, 15, 20, 22, 23, 30, 32, 33, 42, 44, 45, 48, 56, 58, 59, 62, 63, 72, 74, 75, 78, 79, 80, 89, 90, 92, 93, 96, 97, 98, 108, 110, 112, 113, 116, 117, 118, 129, 132, 134, 135, 138, 139, 140, 143, 152, 156, 158, 159, 162, 163, 164, 167, 168, 177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 r(1) = 1 r(2) = 2, so that a(1) = 2 r(3) = 2 + 1 r(4) = 4 r(5) = 4 + 1 r(6) = 6, so that a(2) = 6 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, A257057, A257058. Sequence in context: A244342 A064212 A056906 * A209249 A047238 A189933 Adjacent sequences:  A257053 A257054 A257055 * A257057 A257058 A257059 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 15 2015 STATUS approved

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Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)