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 A257022 Trace of n in the quarter-sum representation of n. 4
 0, 1, 2, 1, 4, 1, 6, 1, 2, 9, 1, 2, 12, 1, 2, 1, 16, 1, 2, 1, 20, 1, 2, 1, 4, 25, 1, 2, 1, 4, 30, 1, 2, 1, 4, 1, 36, 1, 2, 1, 4, 1, 42, 1, 2, 1, 4, 1, 6, 49, 1, 2, 1, 4, 1, 6, 56, 1, 2, 1, 4, 1, 6, 1, 64, 1, 2, 1, 4, 1, 6, 1, 72, 1, 2, 1, 4, 1, 6, 1, 2, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Every positive integer is a sum of at most four distinct quarter squares, of which the least term is the trace; see A257019. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 EXAMPLE Quarter-square representations: r(0) = 0, so a(0) = 0 r(1) = 1, so a(1) = 1 r(2) = 2, so a(2) = 2 r(3) = 2 + 1, so a(3) = 1 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[200]; r[0] = {0}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]]; Table[Last[r[n]], {n, 0, 3 z}] (* A257022 *) CROSSREFS Cf. A002620, A257019, A257020, A257021, A257023. Sequence in context: A295127 A076512 A128707 * A214721 A324384 A329641 Adjacent sequences:  A257019 A257020 A257021 * A257023 A257024 A257025 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 15 2015 STATUS approved

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Last modified February 22 08:42 EST 2020. Contains 332133 sequences. (Running on oeis4.)