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 A052923 Expansion of (1-x)/(1 - x - 4*x^2). 3
 1, 0, 4, 4, 20, 36, 116, 260, 724, 1764, 4660, 11716, 30356, 77220, 198644, 507524, 1302100, 3332196, 8540596, 21869380, 56031764, 143509284, 367636340, 941673476, 2412218836, 6178912740, 15827788084, 40543439044, 103854591380 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS First differences of A006131. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 908 Index entries for linear recurrences with constant coefficients, signature (1,4). FORMULA G.f.: (1-x)/(1 - x - 4*x^2). a(n) = a(n-1) + 4*a(n-2), with a(0)=1, a(1)=0. a(n) = Sum_{alpha=RootOf(-1+z+4*z^2)} (1/17)*(-1+9*alpha)*alpha^(-1-n). If p[1]=0, and p[i]=4, ( i>1), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det A. - Milan Janjic, Apr 29 2010 MAPLE spec := [S, {S=Sequence(Prod(Sequence(Z), Z, Union(Z, Z, Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20); seq(coeff(series((1-x)/(1 -x -4*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 16 2019 MATHEMATICA LinearRecurrence[{1, 4}, {1, 0}, 30] (* G. C. Greubel, Oct 16 2019 *) PROG (PARI) my(x='x+O('x^30)); Vec((1-x)/(1 -x -4*x^2)) \\ G. C. Greubel, Oct 16 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x)/(1 -x -4*x^2) )); // G. C. Greubel, Oct 16 2019 (Sage) def A052923_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1-x)/(1 -x -4*x^2)).list() A052923_list(30) # G. C. Greubel, Oct 16 2019 (GAP) a:=[1, 0];; for n in [3..30] do a[n]:=a[n-1]+4*a[n-2]; od; a; # G. C. Greubel, Oct 16 2019 CROSSREFS Cf. A006131, A026581. Sequence in context: A165559 A180967 A231884 * A321691 A014433 A191366 Adjacent sequences:  A052920 A052921 A052922 * A052924 A052925 A052926 KEYWORD easy,nonn 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 June 5 01:27 EDT 2020. Contains 334828 sequences. (Running on oeis4.)