A070207 Expansion of (1-x-5*x^2)/(1-3*x-2*x^2-x^3).

1, 2, 3, 14, 50, 181, 657, 2383, 8644, 31355, 113736, 412562, 1496513, 5428399, 19690785, 71425666, 259086967, 939803018, 3409008654, 12365718965, 44854977221, 162705378247, 590191808148, 2140841158159, 7765612469020, 28168711531526, 102178200690777

Offset: 0

Author

N. J. A. Sloane, Sep 18 2008

Keywords

• nonn
• easy

Comments

The old entry with this sequence number was a duplicate of A024155.

References

• Benoit Rittaud, Elise Janvresse, Emmanuel Lesigne and Jean-Christophe Novelli, Quand les maths se font discrètes, Le Pommier, 2008 (ISBN 978-2-7465-0370-0). See pp. 42ff.

Links

• Robert Israel, Table of n, a(n) for n = 0..1770
• Index entries for linear recurrences with constant coefficients, signature (3,2,1).

Programs

Magma

I:=[1,2,3]; [n le 3 select I[n] else 3*Self(n-1)+2*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 28 2015

Maple

f:= gfun:-rectoproc({-a(n+3)+3*a(n+2)+2*a(n+1)+a(n), a(0) = 1, a(1) = 2, a(2) = 3},a(n),remember):
map(f, [$0..50]); # Robert Israel, Dec 28 2015

Mathematica

CoefficientList[Series[(1-x-5x^2)/(1-3x-2x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{3,2,1},{1,2,3},40] (* Harvey P. Dale, Feb 01 2013 *)

PARI

Vec((1-x-5*x^2)/(1-3*x-2*x^2-x^3) + O(x^100)) \\ Altug Alkan, Dec 27 2015

Formula

a(0)=1, a(1)=2, a(2)=3, a(n) = 3*a(n-1)+2*a(n-2)+a(n-3). - Harvey P. Dale, Feb 01 2013