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 1-3 of 3 results.

A110213 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = 1, a(1) = -7, a(2) = 35.

Original entry on oeis.org

1, -7, 35, -169, 803, -3805, 18011, -85237, 403355, -1908709, 9032123, -42740485, 202250171, -957058117, 4528847675, -21430737349, 101411338043, -479883604165, 2270833596731, -10745699955397, 50849198151995, -240620989179589, 1138630746165563, -5388058541915845
Offset: 0

Views

Author

Creighton Dement, Jul 16 2005

Keywords

Links

Crossrefs

Cf. A110210, A110211, A110212.

Programs

  • Maple
    seriestolist(series((-1+2*x)/((x-1)*(6*x^2+6*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2baseksumseq[A*B] with A = + 'i + 'ii' + 'ij' + 'ik' and B = + .5'i - .5'j + .5'k + .5i' + .5j' - .5k' - .5'ij' - .5'ik' + .5'ji' + .5'ki' Sumtype is set to: sum[(Y[0], Y[1], Y[2]),mod(3)
  • Mathematica
    LinearRecurrence[{-5,0,6},{1,-7,35},30] (* Harvey P. Dale, Mar 01 2015 *)

Formula

G.f. (-1+2*x)/((x-1)*(6*x^2+6*x+1))
a(x)=(3-Sqrt[3]+(7-8*Sqrt[3])(-3+Sqrt[3])^x+(-3-Sqrt[3])^x (-10+9*Sqrt[3]))/(13*(-3+Sqrt[3])). - Harvey P. Dale, Mar 01 2015

A110210 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 1, a(2) = -5.

Original entry on oeis.org

-1, 1, -5, 19, -89, 415, -1961, 9271, -43865, 207559, -982169, 4647655, -21992921, 104071591, -492472025, 2330402599, -11027583449, 52183085095, -246933009881, 1168499548711, -5529399232985, 26165398105639, -123815993235929, 585903570781735, -2772525465274841
Offset: 0

Views

Author

Creighton Dement, Jul 16 2005

Keywords

Links

Crossrefs

Cf. A086405, A094433, A110211, A110212, A110213.

Programs

  • Maple
    seriestolist(series((1+4*x)/((x-1)*(6*x^2+6*x+1)), x=0,25));
  • Mathematica
    LinearRecurrence[{-5,0,6},{-1,1,-5},30] (* or *) CoefficientList[ Series[ (1+4*x)/(-1-5*x+6*x^3),{x,0,30}],x] (* Harvey P. Dale, Nov 09 2014 *)

Formula

Superseeker finds: a(n+1) - a(n) = ((-1)^n)*A094433(n+2); a(n+2) - a(n) = ((-1)^(n+1))*A086405(n+1).
G.f.: (4*x+1)/(6*x^3-5*x-1). - Harvey P. Dale, Nov 09 2014

A110211 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 3, a(2) = -15.

Original entry on oeis.org

-1, 3, -15, 69, -327, 1545, -7311, 34593, -163695, 774609, -3665487, 17345265, -82078671, 388400433, -1837930575, 8697180849, -41155501647, 194749924785, -921566538831, 4360899684273, -20635998872655, 97650595130289, -462087577545807, 2186621894493105
Offset: 0

Views

Author

Creighton Dement, Jul 16 2005

Keywords

Links

Crossrefs

Cf. A110210, A110212, A110213.

Programs

  • Maple
    seriestolist(series((1+2*x)/((x-1)*(6*x^2+6*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1kbasesumseq[A*B] with A = + 'i + 'ii' + 'ij' + 'ik' and B = + .5'i - .5'j + .5'k + .5i' + .5j' - .5k' - .5'ij' - .5'ik' + .5'ji' + .5'ki' Sumtype is set to: sum[(Y[0], Y[1], Y[2]),mod(3)
  • Mathematica
    LinearRecurrence[{-5,0,6},{-1,3,-15},30] (* Harvey P. Dale, Mar 28 2012 *)

Formula

G.f.: (1+2*x)/((x-1)*(6*x^2+6*x+1)).
a(n) = (-3+(-3-sqrt(3))^n*(-5-2*sqrt(3))+(-3+sqrt(3))^n*(-5+2*sqrt(3)))/13. - Harvey P. Dale, Mar 28 2012 [corrected by Jason Yuen, Aug 29 2025]
Showing 1-3 of 3 results.

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