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A070207 Expansion of (1-x-5*x^2)/(1-3*x-2*x^2-x^3). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

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 *)

PROG

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

(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

CROSSREFS

Sequence in context: A294495 A188289 A153741 * A268559 A270707 A141148

Adjacent sequences:  A070204 A070205 A070206 * A070208 A070209 A070210

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 18 2008

STATUS

approved

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Last modified November 22 08:57 EST 2017. Contains 295076 sequences.