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A097356
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Number of partitions of n into parts not greater than sqrt(n).
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4
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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; internal format)
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OFFSET
| 1,4
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MATHEMATICA
| Table[Length[IntegerPartitions[n, Floor[Sqrt[n]]]], {n, 70}] (* From 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 *)
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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
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CROSSREFS
| Cf. A194020, A000196, A000041, A097355.
Sequence in context: A120196 A196179 A120188 * A083522 A108942 A025561
Adjacent sequences: A097353 A097354 A097355 * A097357 A097358 A097359
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 08 2004
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