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A077939 Expansion of 1/(1-2*x-x^2-x^3). 9
1, 2, 5, 13, 33, 84, 214, 545, 1388, 3535, 9003, 22929, 58396, 148724, 378773, 964666, 2456829, 6257097, 15935689, 40585304, 103363394, 263247781, 670444260, 1707499695, 4348691431, 11075326817, 28206844760, 71837707768, 182957587113, 465959726754 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..29.

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

FORMULA

a(n) = abs(A077986(n)) = A077849(n)-A077849(n-1) = |A077922(n)|+|A077922(n-1)| = sum(k=0, n, A077997(k)). - Ralf Stephan, Feb 02 2004

a(n)=sum(m=1..n+1, sum(k=0..n-m+1, (sum(j=0..k, binomial(j,n-m-3*k+2*j+1)*binomial(k,j)))* binomial(m+k-1,m-1))). [From Vladimir Kruchinin, Oct 11 2011]

G.f. for sequence with 1 prepended: 1/( 1 - sum(k>=0,  x*(x+x^2+x^3)^k ) ). [Joerg Arndt, Sep 30 2012]

G.f.: Q(0)/2, where Q(k) = 1 + 1/(1- x*(4*k+2 + x+x^2)/(x*(4*k+4 + x+x^2) + 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013

MATHEMATICA

CoefficientList[Series[1/(1-2*x-x^2-x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 1, 1}, {1, 2, 5}, 40] (* Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)

PROG

(Maxima)

a(n):=sum(sum((sum(binomial(j, n-m-3*k+2*j+1)*binomial(k, j), j, 0, k))* binomial(m+k-1, m-1), k, 0, n-m+1), m, 1, n+1); [From Vladimir Kruchinin, Oct 11 2011]

(PARI) Vec(1/(1-2*x-x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Sequence in context: A120925 A086588 * A077986 A007020 A080888 A052988

Adjacent sequences:  A077936 A077937 A077938 * A077940 A077941 A077942

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified August 28 13:24 EDT 2015. Contains 261122 sequences.