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 A257019 Numbers whose quarter-square representation consists of two terms. 10
 3, 5, 7, 8, 10, 11, 13, 14, 17, 18, 21, 22, 24, 26, 27, 29, 31, 32, 34, 37, 38, 40, 43, 44, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 65, 66, 68, 70, 73, 74, 76, 78, 82, 83, 85, 87, 91, 92, 94, 96, 99, 101, 102, 104, 106, 109, 111, 112, 114, 116, 119, 122, 123 (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). LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE Quarter-square representations: r(0) = 0, one term r(1) = 1, one term r(3) = 2 + 1, two terms, so a(1) = 3 MATHEMATICA z = 100; 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, 4 z}]; (* A257023 *) Flatten[-1 + Position[u, 1]]; (* A002620 *) Flatten[-1 + Position[u, 2]]; (* A257019 *) Flatten[-1 + Position[u, 3]]; (* A257020 *) Flatten[-1 + Position[u, 4]]; (* A257021 *) CROSSREFS Cf. A002620, A257020, A257021, A257023. Sequence in context: A049068 A185602 A225554 * A071977 A183423 A109404 Adjacent sequences:  A257016 A257017 A257018 * A257020 A257021 A257022 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 15 2015 STATUS approved

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Last modified February 29 01:11 EST 2020. Contains 332353 sequences. (Running on oeis4.)