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A257020 Numbers whose quarter-square representation consists of three terms. 7
15, 19, 23, 28, 33, 35, 39, 41, 45, 47, 52, 54, 59, 61, 63, 67, 69, 71, 75, 77, 79, 80, 84, 86, 88, 89, 93, 95, 97, 98, 103, 105, 107, 108, 113, 115, 117, 118, 120, 124, 126, 128, 129, 131, 135, 137, 139, 140, 142, 143, 147, 149, 151, 152, 154, 155, 159, 161 (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(15) = 12 + 2 + 1, three terms; a(1) = 15

r(19) = 16 + 2 + 1, three terms; a(2) = 19

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, A257019, A257021, A257023 (trace), A257024 (number of square in quarter-square representation).

Sequence in context: A225861 A329184 A077349 * A234849 A164564 A211329

Adjacent sequences:  A257017 A257018 A257019 * A257021 A257022 A257023

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 15 2015

STATUS

approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)