A077970 -id:A077970 - cp's OEIS frontend

A077946 Expansion of 1/(1 - x - 2x^2 - 2x^3).

1, 1, 3, 7, 15, 35, 79, 179, 407, 923, 2095, 4755, 10791, 24491, 55583, 126147, 286295, 649755, 1474639, 3346739, 7595527, 17238283, 39122815, 88790435, 201512631, 457339131, 1037945263, 2355648787, 5346217575, 12133405675, 27537138399, 62496384899, 141837473047

Offset: 0

N. J. A. Sloane, Nov 17 2002

Discarding the first 1 = INVERT transform of [1,2,2,0,0,0,...]. - Gary W. Adamson, Feb 16 2010

Index entries for linear recurrences with constant coefficients, signature (1,2,2).

Cf. A077970.

Vec(1/(1-x-2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

a(n) = leftmost term in M^n * [1 0 0], where M = the 3X3 matrix [1 1 1 / 2 0 0 / 0 1 0]. a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3). a(n)/a(n-1) tends to 2.26953084..., an eigenvalue of M and a root of the characteristic polynomial x^3 - x^2 - 2x - 2. a(6) = 79 = 35 + 2*15 + 2*7 = a(5) + 2*a(4) + 2*a(3). - Gary W. Adamson, Dec 21 2004

A078040 Expansion of (1-x)/(1+x-2x^2+2x^3).

Original entry on oeis.org

1, -2, 4, -10, 22, -50, 114, -258, 586, -1330, 3018, -6850, 15546, -35282, 80074, -181730, 412442, -936050, 2124394, -4821378, 10942266, -24833810, 56361098, -127913250, 290303066, -658851762, 1495284394, -3393594050, 7701866362, -17479623250, 39670544074, -90033523298

Offset: 0

N. J. A. Sloane, Nov 17 2002

Index entries for linear recurrences with constant coefficients, signature (-1,2,-2).

First differences of A077970.

CoefficientList[Series[(1-x)/(1+x-2x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{-1,2,-2},{1,-2,4},40] (* Harvey P. Dale, Dec 09 2011 *)

Vec((1-x)/(1+x-2*x^2+2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

a(0) = 1, a(1) = -2, a(2) = 4, a(n) = -a(n-1) + 2*a(n-2) - 2*a(n-3) for n > 2. - Harvey P. Dale, Dec 09 2011

a(n) = A077970(n)-A077970(n-1). - R. J. Mathar, Mar 19 2025

A077900 Expansion of (1-x)^(-1)/(1+x-2x^2+2x^3).

Original entry on oeis.org

1, 0, 3, -4, 11, -24, 55, -124, 283, -640, 1455, -3300, 7491, -17000, 38583, -87564, 198731, -451024, 1023615, -2323124, 5272403, -11965880, 27156935, -61633500, 139879131, -317460000, 720485263, -1635163524, 3711054051, -8422351624, 19114786775, -43381598124, 98455874923

Offset: 0

N. J. A. Sloane, Nov 17 2002

Index entries for linear recurrences with constant coefficients, signature (0,3,-4,2).

A077970(n) = a(n)-a(n-1). - R. J. Mathar, Feb 28 2019

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A077946 Expansion of 1/(1 - x - 2x^2 - 2x^3).

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A078040 Expansion of (1-x)/(1+x-2x^2+2x^3).

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A077900 Expansion of (1-x)^(-1)/(1+x-2x^2+2x^3).

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cp's OEIS Frontend

A077946 Expansion of 1/(1 - x - 2*x^2 - 2*x^3).

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A078040 Expansion of (1-x)/(1+x-2*x^2+2*x^3).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A077900 Expansion of (1-x)^(-1)/(1+x-2*x^2+2*x^3).

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A077946 Expansion of 1/(1 - x - 2x^2 - 2x^3).

A078040 Expansion of (1-x)/(1+x-2x^2+2x^3).

A077900 Expansion of (1-x)^(-1)/(1+x-2x^2+2x^3).