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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.)