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A052965 Expansion of (1-x)/(1-3x-4x^2+4x^3). 0
1, 2, 10, 34, 134, 498, 1894, 7138, 26998, 101970, 385350, 1455938, 5501334, 20786354, 78540646, 296762018, 1121303222, 4236795154, 16008550278, 60487618562, 228549876182, 863565901682, 3262946735526, 12328904308578 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1036

Index entries for linear recurrences with constant coefficients, signature (3,4,-4)

FORMULA

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

Recurrence: {a(0)=1, a(1)=2, a(2)=10, 4*a(n)-4*a(n+1)-3*a(n+2)+a(n+3)=0}

Sum(-1/158*(-17-49*_alpha+40*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-4*_Z^2+4*_Z^3))

MAPLE

spec := [S, {S=Sequence(Prod(Union(Z, Z, Sequence(Z)), Union(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

MATHEMATICA

CoefficientList[Series[(1-x)/(1-3x-4x^2+4x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, 4, -4}, {1, 2, 10}, 40] (* Harvey P. Dale, Dec 01 2016 *)

CROSSREFS

Sequence in context: A119193 A124634 A192378 * A108924 A221492 A116898

Adjacent sequences:  A052962 A052963 A052964 * A052966 A052967 A052968

KEYWORD

easy,nonn,changed

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved

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Last modified December 5 19:19 EST 2016. Contains 278770 sequences.