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A002125
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a(n) = Sum_{k=0..n} f(k)*f(n-k) where f(k) = A002124(k).
(Formerly M0024 N0006)
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3
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1, 0, 0, 2, 0, 2, 3, 2, 6, 4, 9, 14, 11, 26, 29, 34, 62, 68, 99, 140, 169, 252, 322, 430, 607, 764, 1059, 1424, 1845, 2546, 3344, 4442, 6002, 7876, 10575, 14058, 18575, 24878, 32842, 43630, 58073, 76658, 101913, 134964, 178468, 236776, 312874, 414094, 547947, 723646
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Arises in studying the Goldbach conjecture.
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REFERENCES
| P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. [Coll. Papers, Vol. II, pp. 354-382] [The sequence I_n]
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..1000
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MAPLE
| M:=120; f:=array(0..M); f[0]:=1; f[1]:=0; f[2]:=0; for n from 3 to M do t1:=0; for k from 2 to n do p := ithprime(k); if p <= n then t1 := t1 + f[n-p]; fi; od: f[n]:=t1; od: # f is A002124
A002125:=array(0..M); for n from 0 to M do A002125[n]:=add(f[t]*f[n-t], t=0..n); od: [seq(A002125[n], n=0..M)];
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CROSSREFS
| Sequence in context: A104513 A033769 A074660 * A171731 A185815 A003987
Adjacent sequences: A002122 A002123 A002124 * A002126 A002127 A002128
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2006
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