cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A105577 a(n) = 2*a(n-1) - 3*a(n-2) + 2*a(n-3) with a(0) = 1, a(1) = 5, a(2) = 6.

Original entry on oeis.org

1, 5, 6, -1, -10, -5, 18, 31, -2, -61, -54, 71, 182, 43, -318, -401, 238, 1043, 570, -1513, -2650, 379, 5682, 4927, -6434, -16285, -3414, 29159, 35990, -22325, -94302, -49649, 138958, 238259, -39654, -516169, -436858, 595483, 1469202, 278239, -2660162, -3216637, 2103690, 8536967
Offset: 0

Views

Author

Creighton Dement, Apr 14 2005

Keywords

Comments

Floretion Algebra Multiplication Program, FAMP Code: 2lesseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e]

Links

Crossrefs

Cf. A002249, A014551, A105578.
Equals (1/4) [A107920(n+4) + 2*A107920(n-1) + 3].

Programs

  • Mathematica
    LinearRecurrence[{2,-3,2},{1,5,6},50] (* Harvey P. Dale, Apr 13 2019 *)

Formula

G.f.: (1+3*x-x^2)/((1-x)*(1-x+2*x^2)). - Colin Barker, Mar 26 2012
E.g.f.: exp(x/2)*(21*exp(x/2) - 7*cos(sqrt(7)*x/2) + 15*sqrt(7)*sin(sqrt(7)*x/2))/14. - Stefano Spezia, May 22 2025

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

Original entry on oeis.org

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

Views

Author

Creighton Dement, Apr 14 2005

Keywords

Comments

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

Crossrefs

Cf. A002249, A014551, A078020, A105577, A105578, A105580.
Cf. Equals (1/2) [A107920(n+4) - 2*A107920(n-1) + 3 ].

Programs

  • Mathematica
    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 *)

Formula

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]

Extensions

Corrected by T. D. Noe, Nov 07 2006

A105580 a(n+3) = a(n) - a(n+1) - a(n+2); a(0) = -5, a(1) = 6, a(2) = 0.

Original entry on oeis.org

-5, 6, 0, -11, 17, -6, -22, 45, -29, -38, 112, -103, -47, 262, -318, 9, 571, -898, 336, 1133, -2367, 1570, 1930, -5867, 5507, 2290, -13664, 16881, -927, -29618, 47426, -18735, -58309, 124470, -84896, -97883, 307249, -294262, -110870, 712381, -895773, 72522, 1535632, -2503927, 1040817, 2998742
Offset: 0

Views

Author

Creighton Dement, Apr 14 2005

Keywords

Comments

Floretion Algebra Multiplication Program, FAMP Code: 2tesforseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e], 1vesforseq = A000004, ForType: 1A.

Examples

			This sequence was generated using the same floretion which generated the sequences A105577, A105578, A105579, etc.. However, in this case a force transform was applied. [Specifically, (a(n)) may be seen as the result of a tesfor-transform of the zero-sequence A000004 with respect to the floretion given in the program code.]

Links

Crossrefs

Cf. A002249, A014551, A078020, A105577, A105578, A105581.

Programs

  • Mathematica
    Transpose[NestList[Join[Rest[#],ListCorrelate[ {1,-1,-1}, #]]&,{-5,6,0},50]][[1]]  (* Harvey P. Dale, Mar 14 2011 *)
CoefficientList[Series[(5-x-x^2)/(x^3-x^2-x-1),{x,0,50}],x]  (* Harvey P. Dale, Mar 14 2011 *)

Formula

G.f. (5-x-x^2)/(x^3-x^2-x-1)
a(n) = A078046(n-1) - A073145(n+3).
a(n) = -5*A057597(n+2) + A057597(n+1)+A057597(n). - R. J. Mathar, Oct 25 2022

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.

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

Views

Author

Creighton Dement, Apr 14 2005

Keywords

Comments

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

Links

Crossrefs

Cf. A105577, A105578, A105579, A105580.
Equals 2*A107920(n) + A107920(n-1) + 1.

Programs

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

Formula

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]
Showing 1-4 of 4 results.

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