The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A111178 Number of partitions of n into positive numbers one less than a square. 7
 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 2, 4, 1, 2, 5, 2, 4, 5, 2, 5, 5, 2, 6, 7, 4, 6, 7, 5, 6, 8, 6, 8, 12, 6, 9, 13, 6, 10, 15, 8, 14, 15, 9, 16, 16, 10, 18, 21, 14, 19, 22, 16, 20, 24, 19, 25, 30, 20, 27, 33, 21, 29, 39, 26, 37, 40, 28, 42, 42, 31, 48 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,16 COMMENTS Also limiting form of the number of representations of n into k positive squares for k decreasing from n to 1, or Table[Count[SumOfSquaresRepresentations[k,n], {a_,__}/;a>0], {n,100,100}, {k,100,40,-1}]. (Franklin T. Adams-Watters: replacing k^2 ones by the value k^2 changes the count by k^2-1). a(n) = A243148(2n,n). - Alois P. Heinz, May 30 2014 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe) FORMULA G.f.: Product_{k>=2} 1/(1-x^(k^2-1)). MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0, b(n, i-1)+ `if`(i^2>n+1, 0, b(n+1-i^2, i)))) end: a:= n-> b(n, isqrt(n)): seq(a(n), n=0..100); # Alois P. Heinz, May 30 2014 MATHEMATICA nn = 100; CoefficientList[Series[Product[1/(1 - x^(k^2 - 1)), {k, 2, nn}], {x, 0, nn}], x] (* corrected by T. D. Noe, Feb 22 2012 *) b[n_, i_] := b[n, i] = If[n==0, 1, If[i<2, 0, b[n, i-1] + If[i^2>n+1, 0, b[n+1-i^2, i]]]]; a[n_] := b[n, Round[Sqrt[n]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 16 2017, after Alois P. Heinz *) PROG (Haskell) a111178 = p \$ tail a005563_list where p _ 0 = 1 p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m -- Reinhard Zumkeller, Apr 02 2014 CROSSREFS Cf. A001156, A078134. Cf. A005563, A319799. Sequence in context: A025432 A025433 A025434 * A279187 A254434 A076845 Adjacent sequences: A111175 A111176 A111177 * A111179 A111180 A111181 KEYWORD easy,nonn AUTHOR Wouter Meeussen, Oct 22 2005 STATUS approved

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

Last modified November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)