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A078010 Expansion of (1-x)/(1-x-x^2-2*x^3). 3
1, 0, 1, 3, 4, 9, 19, 36, 73, 147, 292, 585, 1171, 2340, 4681, 9363, 18724, 37449, 74899, 149796, 299593, 599187, 1198372, 2396745, 4793491, 9586980, 19173961, 38347923, 76695844, 153391689, 306783379, 613566756, 1227133513, 2454267027, 4908534052 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 2).

FORMULA

a(0)=1, a(1)=0, a(2)=1, a(n)=a(n-1)+a(n-2)+2*a(n-3) for n>2 . - Philippe Deléham, Sep 19 2006

a(n)+a(n+1)=A122552(n+1) . - Philippe Deléham, Sep 25 2006

If p[1]=0, p[2]=1, p[i]=3, (i>2), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det A. [Milan Janjic, May 02 2010]

For n>3 = A077947(n-2) + 2*A077947(n-3), with A077947 beginning (1, 2, 5, 9, 18, 37,...); "1" has offset 1. [Gary W. Adamson, May 13 2013]

EXAMPLE

a(6) = 19 = A077947(4) + 2*A077947(3) = 9 + 2*5 = 19

MATHEMATICA

CoefficientList[Series[(1-x)/(1-x-x^2-2*x^3), {x, 0, 50}], x]  (* Harvey P. Dale, Mar 17 2011 *)

LinearRecurrence[{1, 1, 2}, {1, 0, 1}, 70] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2012 *)

PROG

(PARI) Vec((1-x)/(1-x-x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Cf. A077947.

Sequence in context: A192288 A028344 A219680 * A291532 A110810 A247579

Adjacent sequences:  A078007 A078008 A078009 * A078011 A078012 A078013

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified January 23 02:40 EST 2019. Contains 319365 sequences. (Running on oeis4.)