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

0,3

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).

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A092836, A092835, A100477, A101822.

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