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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A097356 Number of partitions of n into parts not greater than sqrt(n). 15
 1, 1, 1, 1, 3, 3, 4, 4, 5, 12, 14, 16, 19, 21, 24, 27, 64, 72, 84, 94, 108, 120, 136, 150, 169, 377, 427, 480, 540, 603, 674, 748, 831, 918, 1014, 1115, 2432, 2702, 3009, 3331, 3692, 4070, 4494, 4935, 5427, 5942, 6510, 7104, 7760, 16475, 18138, 19928, 21873, 23961 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..20000 Vaclav Kotesovec, Graph - the asymptotic ratio FORMULA a(n^2) ~ c * d^n / n^2, where d = A258268 = 9.153370192454122461948530292401354... and c = 0.1582087202672504149766310999238... [see A206226, constant c(1)]. The upper bound of a(n) is c * d^sqrt(n) / n, see graph. For the lower bound, the constant c = 0.088154883798697116... (conjectured). - Vaclav Kotesovec, Jan 08 2024 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+b(n-i, min(n-i, i)))) end: a:= n-> b(n, (r-> `if`(r*r>n, r-1, r))(isqrt(n))): seq(a(n), n=0..100); # Alois P. Heinz, Aug 02 2018 MATHEMATICA Table[Length[IntegerPartitions[n, Floor[Sqrt[n]]]], {n, 70}] (* Harvey P. Dale, May 11 2011 *) f[n_, 1] := 1; f[1, k_] := 1; f[n_, k_] := f[n, k] = If[k > n, f[n, k - 1], f[n, k - 1] + f[n - k, k]]; Table[ f[n, Floor[Sqrt[n]]], {n, 53}] (* Robert G. Wilson v, Aug 13 2011 *) PROG (Haskell) a097356 n = p [1..a000196 n] n where p [] _ = 0 p _ 0 = 1 p ks'@(k:ks) m | m < k = 0 | otherwise = p ks' (m - k) + p ks m -- Reinhard Zumkeller, Aug 12 2011 (PARI) a(n, k=sqrtint(n))=if(min(n, k)<2, 1, sum(i=1, min(k, n), a(n-i, i))) \\ Charles R Greathouse IV, Aug 12 2011 CROSSREFS Cf. A194020, A000196, A000041, A097355. Sequence in context: A120188 A369217 A369218 * A083522 A355067 A108942 Adjacent sequences: A097353 A097354 A097355 * A097357 A097358 A097359 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 08 2004 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 August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)