A105580 -id:A105580 - cp's OEIS frontend

A105579 a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 3, a(2) = 4.

1, 3, 4, 1, -4, -3, 8, 17, 4, -27, -32, 25, 92, 45, -136, -223, 52, 501, 400, -599, -1396, -195, 2600, 2993, -2204, -8187, -3776, 12601, 20156, -5043, -45352, -35263, 55444, 125973, 15088, -236855, -267028, 206685, 740744, 327377, -1154108, -1808859, 499360, 4117081, 3118364, -5115795, -11352520

Offset: 0

Creighton Dement, Apr 14 2005

Floretion Algebra Multiplication Program, FAMP Code: famseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e]

Cf. A002249, A014551, A078020, A105577, A105578, A105580.

Cf. Equals (1/2) [A107920(n+4) - 2*A107920(n-1) + 3 ].

Table[(3 - ((1-I*Sqrt[7])^n + (1+I*Sqrt[7])^n)/2^n)/2 // Simplify, {n, 1, 50}] (* Jean-François Alcover, Jun 04 2017 *)

a(n+1) - a(n) = A002249(n).

a(n) = 2*a(n-1)-3*a(n-2)+2*a(n-3). G.f.: (1+x+x^2)/((1-x)*(1-x+2*x^2)). [Colin Barker, Mar 27 2012]

Corrected by T. D. Noe, Nov 07 2006

A105576 a(n) = 2a(n-1) - 3a(n-2) + 2*a(n-3) with a(0) = 3, a(1) = 4, a(2) = 0.

Original entry on oeis.org

3, 4, 0, -6, -4, 10, 20, 2, -36, -38, 36, 114, 44, -182, -268, 98, 636, 442, -828, -1710, -52, 3370, 3476, -3262, -10212, -3686, 16740, 24114, -9364, -57590, -38860, 76322, 154044, 1402, -306684, -309486, 303884, 922858, 315092, -1530622, -2160804, 900442, 5222052, 3421170

Offset: 0

Creighton Dement, Apr 14 2005

Floretion Algebra Multiplication Program, FAMP Code: 1vesseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e]

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

Cf. A105577, A105578, A105579, A105580.

Equals 2*A107920(n) + A107920(n-1) + 1.

LinearRecurrence[{2,-3,2},{3,4,0},50] (* Harvey P. Dale, Jul 05 2022 *)

2*a(n) = A105225(n) + A105577(n) + 4*((-1)^n)*A001607(n+1)

G.f.: (3-2x+x^2)/((1-x)(1-x+2x^2)). a(n)=1+A107920(n)+2*A107920(n+1). [From R. J. Mathar, Feb 04 2009]

cp's OEIS Frontend

A105579 a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 3, a(2) = 4.

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A105576 a(n) = 2a(n-1) - 3a(n-2) + 2*a(n-3) with a(0) = 3, a(1) = 4, a(2) = 0.

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cp's OEIS Frontend

A105579 a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 3, a(2) = 4.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

Extensions

A105576 a(n) = 2*a(n-1) - 3*a(n-2) + 2*a(n-3) with a(0) = 3, a(1) = 4, a(2) = 0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A105576 a(n) = 2a(n-1) - 3a(n-2) + 2*a(n-3) with a(0) = 3, a(1) = 4, a(2) = 0.