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 A257057 Numbers k such that (# squares) = (# nonsquares) in the quarter-squares representation of k. 3
 3, 7, 11, 13, 18, 21, 24, 27, 31, 34, 38, 43, 46, 51, 55, 57, 60, 66, 70, 73, 76, 83, 87, 91, 94, 99, 102, 106, 111, 114, 119, 123, 127, 133, 136, 141, 146, 150, 157, 160, 165, 171, 175, 181, 183, 186, 191, 198, 202, 208, 211, 214, 219, 227, 231, 237, 241 (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 r(3) = 2 + 1, so that a(1) = 3 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, A257058. Sequence in context: A045417 A260379 A045418 * A310197 A090456 A070303 Adjacent sequences:  A257054 A257055 A257056 * A257058 A257059 A257060 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 15 2015 STATUS approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)