A100550 a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3), for n>3, otherwise a(n) = n.

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

Offset: 0

Author

gamo (gamo(AT)telecable.es), Nov 27 2004

Keywords

• easy
• nonn

Comments

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

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,3).

Crossrefs

Cf. A092836, A092835, A100477, A101822.

Programs

Magma

[n le 3 select n-1 else Self(n-1) +2*Self(n-2) +3*Self(n-3): n in [1..41]]; // G. C. Greubel, Mar 27 2023

Mathematica

LinearRecurrence[{1,2,3},{0,1,2},40] (* Harvey P. Dale, Mar 19 2023 *)

Perl

perl -e '@a=(0,1,2);for(3..30){$a[$]=$a[$-1]+2*$a[$-2]+3*$a[$-3];} print "@a ";'

SageMath

@CachedFunction
def a(n): # a = A100550
    if (n<3): return n
    else: return a(n-1) + 2*a(n-2) + 3*a(n-3)
[a(n) for n in range(41)] # G. C. Greubel, Mar 27 2023

Formula

From R. J. Mathar, Aug 22 2008: (Start)

O.g.f.: x*(1+x)/(1-x-2*x^2-3*x^3).

a(n) = A101822(n-1) + A101822(n-2). (End)