A089883 -id:A089883

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A089932

G.f.: (1-x)^5/((-1+4*x-3*x^2+x^3)*(1-3*x+x^2)*(-1+2*x)).

+10
3

1, 4, 16, 60, 215, 747, 2539, 8491, 28049, 91782, 298109, 962594, 3093687, 9905444, 31619072, 100681587, 319944693, 1015039586, 3215903436, 10177462312, 32179381609, 101668695088, 321014982282, 1013068488800, 3195703133266, 10077204123667, 31767718475161

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Harvey P. Dale, 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. See Th. 3.6, case k=4.

Index entries for linear recurrences with constant coefficients, signature (9,-30,46,-34,13,-2)

MATHEMATICA

CoefficientList[Series[(1-x)^5/((-1+4x-3x^2+x^3)(1-3x+x^2)(-1+2x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{9, -30, 46, -34, 13, -2}, {1, 4, 16, 60, 215, 747}, 30] (* Harvey P. Dale, May 20 2015 *)

CROSSREFS

Cf. A061667, A089883, A089947.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 18 2004

STATUS

approved

A089947

G.f.: (1-x)^9/((1-5*x+6*x^2-4*x^3+x^4)*(-1+4*x-3*x^2+x^3)*(1-3*x+x^2)*(-1+2*x)).

+10
1

1, 5, 25, 115, 500, 2092, 8512, 33910, 132892, 514079, 1968021, 7470434, 28160354, 105542777, 393672627, 1462503264, 5414896000, 19991387639, 73628208598, 270614786791, 992880076249, 3637400475618, 13308475404934, 48639360355243, 177597694845849

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

A. Burstein and T. Mansour, Words restricted by 3-letter ..., Annals. Combin., 7 (2003), 1-14; see Th. 3.6, case k=5.

LINKS

Table of n, a(n) for n=0..24.

A. Burstein and T. Mansour, Words restricted by 3-letter ....

Index entries for linear recurrences with constant coefficients, signature (14, -81, 254, -481, 588, -485, 270, -98, 21, -2).

MATHEMATICA

CoefficientList[Series[(1-x)^9/((1-5x+6x^2-4x^3+x^4)(-1+4x-3x^2+x^3)(1-3x+x^2)(-1+2x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{14, -81, 254, -481, 588, -485, 270, -98, 21, -2}, {1, 5, 25, 115, 500, 2092, 8512, 33910, 132892, 514079}, 30] (* Harvey P. Dale, Oct 03 2015 *)