A099213 -id:A099213 - cp's OEIS frontend

A099212 a(n) = -2a(n-1) + 4a(n-3), with a(0) = 1, a(1) = a(2) = 0.

1, 0, 0, 4, -8, 16, -16, 0, 64, -192, 384, -512, 256, 1024, -4096, 9216, -14336, 12288, 12288, -81920, 212992, -376832, 425984, 0, -1507328, 4718592, -9437184, 12845056, -6815744, -24117248, 99614720, -226492416, 356515840, -314572800, -276824064, 1979711488

Offset: 0

Paul Barry, Oct 06 2004

Binomial transform is A099213.

Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,0,4).

Cf. A099211.

LinearRecurrence[{-2,0,4},{1,0,0},40] (* Harvey P. Dale, May 02 2019 *)

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

a(31) onwards from Andrew Howroyd, Mar 19 2025

A099214 a(n)=4a(n-1)-4a(n-2)+4a(n-3).

Original entry on oeis.org

1, 2, 4, 12, 40, 128, 400, 1248, 3904, 12224, 38272, 119808, 375040, 1174016, 3675136, 11504640, 36014080, 112738304, 352915456, 1104764928, 3458351104, 10826006528, 33889681408, 106088103936, 332097716224, 1039597174784

Offset: 0

Paul Barry, Oct 06 2004

Binomial transform of A099213.

Cf. A073724.

G.f.: (1-2x)/((1-2x)^2-4x^3); a(n)=sum{k=0..floor(n/3), binomial(n-k, 2k)4^k*2^(n-3k)}.

A123102 a(0)=1, a(1)=0, a(2)=1, a(n) = a(n-1) + a(n-2) + 3*a(n-3).

Original entry on oeis.org

1, 0, 1, 4, 5, 12, 29, 56, 121, 264, 553, 1180, 2525, 5364, 11429, 24368, 51889, 110544, 235537, 501748, 1068917, 2277276, 4851437, 10335464, 22018729, 46908504, 99933625, 212898316, 453557453, 966256644, 2058509045, 4385438048

Offset: 0

Philippe Deléham, Sep 27 2006

Index entries for linear recurrences with constant coefficients, signature (1,1,3).

Cf. A099213.

LinearRecurrence[{1,1,3},{1,0,1},40] (* Harvey P. Dale, May 04 2018 *)

Vec((1-x)/(1-x-x^2-3*x^3) + O(x^40)) \\ Michel Marcus, Aug 07 2022

a(n) + a(n+1) = A099213(n+1).
G.f.: (1-x)/(1-x-x^2-3*x^3).
If p[1]=0, p[2]=1, p[i]=4, (i>2), 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, May 02 2010

Corrected by T. D. Noe, Nov 07 2006

cp's OEIS Frontend

A099212 a(n) = -2a(n-1) + 4a(n-3), with a(0) = 1, a(1) = a(2) = 0.

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A099214 a(n)=4a(n-1)-4a(n-2)+4a(n-3).

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Formula

A123102 a(0)=1, a(1)=0, a(2)=1, a(n) = a(n-1) + a(n-2) + 3*a(n-3).

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cp's OEIS Frontend

A099212 a(n) = -2*a(n-1) + 4*a(n-3), with a(0) = 1, a(1) = a(2) = 0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A099214 a(n)=4a(n-1)-4a(n-2)+4a(n-3).

Views

Author

Keywords

Comments

Crossrefs

Formula

A123102 a(0)=1, a(1)=0, a(2)=1, a(n) = a(n-1) + a(n-2) + 3*a(n-3).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A099212 a(n) = -2a(n-1) + 4a(n-3), with a(0) = 1, a(1) = a(2) = 0.