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A123893 Expansion of g.f.: (1+x^2)*(1+2*x^2)*(1+3*x^2)/(1-4*x+6*x^2-18*x^3 +11*x^4-22*x^5+6*x^6-6*x^7). 4
1, 4, 16, 58, 208, 750, 2708, 9772, 35256, 127210, 459012, 1656228, 5976040, 21562946, 77804232, 280736004, 1012961416, 3655002994, 13188110940, 47585806908, 171700784680, 619536821778, 2235434596432, 8065973894524, 29103931264328, 105013830473538 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of words of length n over (0,1,2,3} which have no factor iji with i>j. - N. J. A. Sloane, May 21 2013

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, Annals. Combin., 7 (2003), 1-14.

Index entries for linear recurrences with constant coefficients, signature (4,-6,18,-11,22,-6,6).

FORMULA

a(0)=1, a(1)=4, a(2)=16, a(3)=58, a(4)=208, a(5)=750, a(6)=2708, a(n)= 4*a(n-1) -6*a(n-2) +18*a(n-3) -11*a(n-4) +22*a(n-5) -6*a(n-6) +6*a(n-7). - Harvey P. Dale, May 20 2012

G.f. can be written 1/(1-x*(1+1/(1+x^2)+1/(1+2*x^2)+1/(1+3*x^2))) which looks more symmetrical. N. J. A. Sloane, May 21 2013

MAPLE

seq(coeff(series((1+x^2)*(1+2*x^2)*(1+3*x^2)/(1-4*x+6*x^2-18*x^3+11*x^4 -22*x^5+6*x^6-6*x^7), x, n+1), x, n), n = 0 .. 30); # G. C. Greubel, Aug 06 2019

MATHEMATICA

CoefficientList[Series[-(1+x^2) (1+2 x^2) (1+3 x^2)/(-1-6 x^2-11 x^4-6 x^6+4 x+18 x^3+22 x^5+6 x^7), {x, 0, 40}], x] (* or *) LinearRecurrence[ {4, -6, 18, -11, 22, -6, 6}, {1, 4, 16, 58, 208, 750, 2708}, 40] Harvey P. Dale, May 20 2012

PROG

(PARI) my(x='x+O('x^30)); Vec((1+x^2)*(1+2*x^2)*(1+3*x^2)/(1-4*x+6*x^2 -18*x^3+11*x^4-22*x^5+6*x^6-6*x^7)) \\ G. C. Greubel, Aug 06 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x^2)*(1+2*x^2)*(1+3*x^2)/(1-4*x+6*x^2-18*x^3+11*x^4-22*x^5+6*x^6-6*x^7) )); // G. C. Greubel, Aug 06 2019

(Sage) ((1+x^2)*(1+2*x^2)*(1+3*x^2)/(1-4*x+6*x^2-18*x^3+11*x^4-22*x^5 +6*x^6-6*x^7)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 06 2019

(GAP) a:=[1, 4, 16, 58, 208, 750, 2708];; for n in [8..30] do a[n]:=4*a[n-1] -6*a[n-2]+18*a[n-3]-11*a[n-4]+22*a[n-5]-6*a[n-6]+6*a[n-7]; od; a; # G. C. Greubel, Aug 06 2019

CROSSREFS

Cf. A005251, A123892, A123894, A225685.

Sequence in context: A123889 A180143 A224128 * A134762 A207276 A047123

Adjacent sequences:  A123890 A123891 A123892 * A123894 A123895 A123896

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 20 2006

STATUS

approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)