The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A257023 Number of terms in the quarter-sum representation of n. 9
 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 2, 1, 2, 2, 3, 2, 3, 2, 1, 2, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 3, 1, 2, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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) = 1 r(3) = 2 + 1, so a(3) = 2 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[Length[r[n]], {n, 0, 3 z}] (* A257022 *) CROSSREFS Cf. A002620, A257019, A257020, A257021, A257022. Sequence in context: A106149 A253607 A212179 * A238894 A054740 A272947 Adjacent sequences:  A257020 A257021 A257022 * A257024 A257025 A257026 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 15 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 21 23:21 EST 2020. Contains 332113 sequences. (Running on oeis4.)