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 1-2 of 2 results.

A262593 Expansion of (1-3*x)^3/((1-x)^4*(1-4*x)).

Original entry on oeis.org

1, -1, -3, -1, 13, 63, 237, 879, 3357, 13135, 52061, 207519, 829037, 3314719, 13256973, 53025423, 212098557, 848390319, 3393556477, 13574220095, 54296873421, 217187485439, 868749932077, 3474999717039, 13899998855133, 55599995405583, 222399981605277, 889599926401759, 3558399705585197
Offset: 0

Views

Author

N. J. A. Sloane, Oct 22 2015

Keywords

Comments

Suggested by A262592.

Crossrefs

Cf. A262592.

Programs

  • PARI
    Vec((1-3*x)^3/((1-x)^4*(1-4*x)) + O(x^40)) \\ Michel Marcus, Oct 23 2015
    
  • PARI
    a(n) = (77+4^(1+n)-84*n-126*n^2+36*n^3)/81 \\ Colin Barker, Oct 23 2015

Formula

a(n + 1) = (1/3)*(12*a(n) - 4*n^3 + 18*n^2 + 4*n - 15), a(0) = 1. - Ilya Gutkovskiy, Oct 22 2015
From Colin Barker, Oct 23 2015: (Start)
a(n) = 8*a(n-1)-22*a(n-2)+28*a(n-3)-17*a(n-4)+4*a(n-5) for n>4.
a(n) = (77+4^(1+n)-84*n-126*n^2+36*n^3)/81.
(End)

A262594 Expansion of (1-2*x)^2/((1-x)^4*(1-4*x)).

Original entry on oeis.org

1, 4, 14, 52, 203, 808, 3232, 12936, 51765, 207100, 828466, 3313964, 13255999, 53024192, 212097028, 848388448, 3393554217, 13574217396, 54296870230, 217187481700, 868749927731, 3474999712024, 13899998849384, 55599995399032, 222399981597853, 889599926393388, 3558399705575802, 14233598822305756
Offset: 0

Views

Author

N. J. A. Sloane, Oct 22 2015

Keywords

Comments

Suggested by A262592.

Crossrefs

Cf. A262592.

Programs

  • Mathematica
    CoefficientList[Series[(1-2x)^2/((1-x)^4(1-4x)),{x,0,40}],x] (* or *) LinearRecurrence[ {8,-22,28,-17,4},{1,4,14,52,203},40] (* Harvey P. Dale, Jul 04 2022 *)
  • PARI
    a(n) = (34+2^(7+2*n)+93*n+18*n^2-9*n^3)/162 \\ Colin Barker, Oct 23 2015
    
  • PARI
    Vec((1-2*x)^2/((1-x)^4*(1-4*x)) + O(x^40)) \\ Colin Barker, Oct 23 2015

Formula

From Colin Barker, Oct 23 2015: (Start)
a(n) = 8*a(n-1)-22*a(n-2)+28*a(n-3)-17*a(n-4)+4*a(n-5) for n>4.
a(n) = (34+2^(7+2*n)+93*n+18*n^2-9*n^3)/162.
(End)
Showing 1-2 of 2 results.