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 A100550 If n>3 a(n)=a(n-1)+2*a(n-2)+3*a(n-3) else a(n)=n 1
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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, 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 REFERENCES Harold Abelson and Gerald Jay Sussman with Julie Sussman, Structure and Interpretation of Computer Programs, MIT Press, 1996 LINKS FORMULA O.g.f.: x(1+x)/(1-x-2x^2-3x^3). a(n)=A101822(n-1)+A101822(n-2). [From R. J. Mathar, Aug 22 2008] EXAMPLE a(3)=1*2+2*1+3*0=4 PROG perl -e '@a=(0, 1, 2); for(3..30){\$a[\$_]=\$a[\$_-1]+2*\$a[\$_-2]+3*\$a[\$_-3]; } print "@a "; ' CROSSREFS Cf. A100477. Cf. A000073, A092836, A092835. Sequence in context: A205500 A342533 A131434 * A329707 A071973 A086424 Adjacent sequences:  A100547 A100548 A100549 * A100551 A100552 A100553 KEYWORD easy,nonn AUTHOR gamo (gamo(AT)telecable.es), Nov 27 2004 STATUS approved

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Last modified July 30 22:16 EDT 2021. Contains 346365 sequences. (Running on oeis4.)