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Search: id:A100550
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| A100550 |
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If n>3 a(n)=a(n-1)+2*a(n-2)+3*a(n-3) else a(n)=n |
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+0
2
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| 0, 1, 2, 4, 11, 25, 59, 142, 335, 796, 1892, 4489, 10661, 25315, 60104, 142717, 338870, 804616, 1910507, 4536349, 10771211, 25575430, 60726899, 144191392, 342371480, 812934961, 1930252097, 4583236459, 10882545536, 25839774745, 61354575194
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A (1,2,3)-weighted version of the tribonacci sequence A000073.
The following are primes: a(2) = 2, a(4) = 11, a(6) = 59 and a(40) = 335593747307843. Semiprimes: a(n) for n = 3,5,7,8,11,12,15,19,20,22,27,35. a(n) is a perfect square for n = 3,5,11. - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 28 2004
A recursive and iterative algorithm for the computation of a(n) appear as Exercise 1.11 in the book Structure and Interpretation of Computer Programs. - Bas Kok (no(AT)spam.com), Jan 31 2008
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REFERENCES
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Harold Abelson and Gerald Jay Sussman with Julie Sussman, Structure and Interpretation of Computer Programs, MIT Press, 1996
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FORMULA
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O.g.f.: x(1+x)/(1-x-2x^2-3x^3). a(n)=A101822(n-1)+A101822(n-2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2008]
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EXAMPLE
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a(3)=1*2+2*1+3*0=4
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PROGRAM
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perl -e '@a=(0, 1, 2); for(3..30){$a[$_]=$a[$_-1]+2*$a[$_-2]+3*$a[$_-3]; } print "@a "; '
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CROSSREFS
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Cf. A100477.
Cf. A000073, A092836, A092835.
Sequence in context: A034485 A018006 A131434 this_sequence A071973 A086424 A122121
Adjacent sequences: A100547 A100548 A100549 this_sequence A100551 A100552 A100553
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KEYWORD
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easy,nonn
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AUTHOR
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gamo (gamo(AT)telecable.es), Nov 27 2004
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