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Search: id:A090764
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| A090764 |
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a(n) = Sum_{pi = partition of n} 2^{number of 1's in pi}. |
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+0
1
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| 2, 5, 11, 24, 50, 104, 212, 431, 870, 1752, 3518, 7057, 14138, 28310, 56661, 113377, 226820, 453728, 907561, 1815259, 3630683, 7261576, 14523405, 29047130, 58094643, 116189764, 232380102, 464760912, 929522671, 1859046381, 3718094000
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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G.f.: (1/(1-2*x))*Product_{m>=2} 1/(1-x^m). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 04 2004
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EXAMPLE
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a(4)=24 because the partitions of 4 are 4(1), 31(2), 22(1), 211(4) and 1111(16). 1+2+1+4+16=24.
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MATHEMATICA
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first Needs["DiscreteMath`Combinatorica`"], then c[n_] := Count[n, 1]; f[n_] := Apply[ Plus, 2^ Map[ c, Partitions[n]]]; Table[ f[n], {n, 1, 31}] (from Robert G. Wilson v Feb 12 2004)
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PROGRAM
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(Java) import java.math.*; import java.io.*; public class A090764 { public static final int LIMIT = 80; public static final BigInteger TWO = new BigInteger("2"); public static void main(String[] args) throws Exception {BigInteger[] a = new BigInteger[LIMIT];
int i, j; PrintStream out = new PrintStream(new FileOutputStream("A090764.txt")); a[0] = BigInteger.ONE; for (i = 1; i < LIMIT; i++)a[i] = a[i - 1].multiply(TWO); for (j = 2; j < LIMIT; j++)for (i = j; i < LIMIT; i++)
a[i] = a[i - 1].multiply(TWO); for (j = 2; j < LIMIT; j++)for (i = j; i < LIMIT; i++) a[i] = a[i].add(a[i - j]); for (i = 0; i < LIMIT; i++)out.print(a[i] + " "); out.print(" "); }} (David Wasserman)
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CROSSREFS
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Sequence in context: A091359 A059776 A091360 this_sequence A027934 A134389 A111297
Adjacent sequences: A090761 A090762 A090763 this_sequence A090765 A090766 A090767
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Feb 01 2004
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 10 2004
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