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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

Table of n, a(n) for n=0..30.

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.)