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!)
 A296338 a(n) = number of partitions of n into consecutive positive squares. 5
 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,25 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 FORMULA a(A034705(n)) >= 1 for n > 1. G.f.: Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k^2). - Ilya Gutkovskiy, Apr 18 2019 EXAMPLE 1 = 1^2,                   so  a(1) = 1.    4 = 2^2,                   so  a(4) = 1.    5 = 1^2 + 2^2,             so  a(5) = 1.    9 = 3^2,                   so  a(9) = 1.   13 = 2^2 + 3^2,             so a(13) = 1.   14 = 1^2 + 2^2 + 3^2,       so a(14) = 1.   16 = 4^2,                   so a(16) = 1.   25 = 3^2 + 4^2 = 5^2,       so a(25) = 2.   29 = 2^2 + 3^2 + 4^2,       so a(29) = 1.   30 = 1^2 + 2^2 + 3^2 + 4^2, so a(30) = 1. MATHEMATICA nMax = 100; t = {0}; Do[k = n; s = 0; While[s = s + k^2; s <= nMax, AppendTo[t, s]; k++], {n, 1, nMax}]; tt = Tally[t]; a[_] = 0; Do[a[tt[[i, 1]]] = tt[[i, 2]], {i, 1, Length[tt]}]; Table[a[n], {n, 1, nMax}] (* Jean-François Alcover, Feb 04 2018, using T. D. Noe's program for A034705 *) PROG (Ruby) def A296338(n)   m = Math.sqrt(n).to_i   ary = Array.new(n + 1, 0)   (1..m).each{|i|     sum = i * i     ary[sum] += 1     i += 1     sum += i * i     while sum <= n       ary[sum] += 1       i += 1       sum += i * i     end   }   ary[1..-1] end p A296338(100) CROSSREFS Cf. A000290, A001227, A034705, A130052, A234304, A297199, A298467, A299173. Sequence in context: A271231 A306798 A086079 * A133703 A073265 A338326 Adjacent sequences:  A296335 A296336 A296337 * A296339 A296340 A296341 KEYWORD nonn AUTHOR Seiichi Manyama, Jan 14 2018 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 September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)