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A099094 a(n) = 3a(n-2) + 3a(n-3), a(0)=1, a(1)=0, a(2)=3. 2
1, 0, 3, 3, 9, 18, 36, 81, 162, 351, 729, 1539, 3240, 6804, 14337, 30132, 63423, 133407, 280665, 590490, 1242216, 2613465, 5498118, 11567043, 24334749, 51195483, 107705376, 226590696, 476702577, 1002888216, 2109879819, 4438772379 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Diagonal sums of A099093.

Counts walks (closed) on the graph G(1-vertex; 2-loop, 2-loop, 2-loop, 3-loop, 3-loop, 3-loop). - David Neil McGrath, Jan 16 2015

Number of compositions of n into parts 2 and 3, each of three sorts. - Joerg Arndt, Feb 14 2015

LINKS

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (0,3,3)

FORMULA

G.f.: 1/(1-3*x^2-3*x^3).

a(n) = sum_{k=0..floor(n/2)} binomial(k, n-2k)*3^k.

Construct the power matrix T(n,j) = [A(n)^*j]*[S(n)^*(j-1)] where A(n) = (0,3,3,0,0...) and S(n) = (0,1,0,0...). (* is convolution operation). Define S^*0 = I. Then T(n,j) counts n-walks containing (j) loops, on the single vertex graph above, and a(n) = sum_{j=1..n} T(n,j). - David Neil McGrath, Jan 16 2015

MATHEMATICA

CoefficientList[Series[1 / (1 - 3 x^2 - 3 x^3), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 16 2015 *)

PROG

(PARI) Vec(1/(1-3*x^2-3*x^3) + O(x^50)) \\ Michel Marcus, Jan 17 2015

CROSSREFS

Sequence in context: A089892 A038221 A099465 * A222169 A222444 A206492

Adjacent sequences:  A099091 A099092 A099093 * A099095 A099096 A099097

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 25 2004

EXTENSIONS

Corrected by Philippe Deléham, Dec 18 2008

STATUS

approved

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Last modified December 3 20:40 EST 2016. Contains 278745 sequences.