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Search: id:A050443
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| A050443 |
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a(0)=4, a(1)=0, a(2)=0, a(3)=3, a(n) = a(n-3) + a(n-4). |
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+0
4
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| 4, 0, 0, 3, 4, 0, 3, 7, 4, 3, 10, 11, 7, 13, 21, 18, 20, 34, 39, 38, 54, 73, 77, 92, 127, 150, 169, 219, 277, 319, 388, 496, 596, 707, 884, 1092, 1303, 1591, 1976, 2395, 2894, 3567, 4371, 5289, 6461, 7938, 9660, 11750, 14399, 17598, 21410, 26149, 31997
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Related to Perrin sequence. a(p) is divisible by p for primes p.
Wells states that Mihaly Bencze (1998) proved the divisibility property for this sequence: that a(n) is always divisible by n when n is prime. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 14 2006
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REFERENCES
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Seen as a puzzle.
American Mathematical Monthly 107 (2000) 281-282 (Solution of Problem 10655),
David Wells, "Prime Numbers, the Most Mysterious Figures in Math", John Wiley & Sons, Inc.; 2005, p. 103.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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G.f.: (4-x^3)/(1-x^3-x^4).
a(n)=(x_1)^n+(x_2)^n+(x_3)^n+(x_4)^n where (x_i) 1<=i<=4 are the roots of x^4=x+1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 27 2003
Let M = the 4 X 4 matrix [0,1,0,0; 0,0,1,0; 0,0,0,1; 1,1,0,0]; then a(n) = the leftmost term of M^n * [4,0,0,3]. Example: a(13) = 13 since M^13 * [4,0,0,3] = [13,21,18,20]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 14 2006
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EXAMPLE
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a(11) = 11 because a(7)=7 and a(8)=4
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CROSSREFS
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Cf. A000040, A001608, A052338.
Cf. A087935, A087936
Sequence in context: A058305 A020808 A091467 this_sequence A036480 A035639 A037214
Adjacent sequences: A050440 A050441 A050442 this_sequence A050444 A050445 A050446
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KEYWORD
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easy,nonn
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AUTHOR
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Tony Davie (ad(AT)dcs.st-and.ac.uk), Dec 23 1999
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EXTENSIONS
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More terms, g.f. from Christian G. Bower (bowerc(AT)usa.net), Dec 23 1999
More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 27 2003
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