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

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]

A110212 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 5, a(2) = -25.

Original entry on oeis.org

-1, 5, -25, 119, -565, 2675, -12661, 59915, -283525, 1341659, -6348805, 30042875, -142164421, 672729275, -3183389125, 15063959099, -71283419845, 337316764475, -1596200067781, 7553299819835, -35742598512325, 169135792154939, -800359161855685, 3787340218204475
Offset: 0

Views

Author

Creighton Dement, Jul 16 2005

Keywords

Comments

Superseeker finds: a(n+1) - a(n) = ((-1)^n)*A030192(n+1) (Scaled Chebyshev U-polynomial evaluated at sqrt(6)/2)

Crossrefs

Cf. A030192, A110210, A110211, A110213.

Programs

  • Maple
    eriestolist(series(1/((x-1)*(6*x^2+6*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2basejsumseq[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)

Formula

G.f.: 1/((x-1)*(6*x^2+6*x+1)).
Showing 1-3 of 3 results.

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