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.

A236582 The number of tilings of an 8 X n floor with 1 X 4 tetrominoes.

Original entry on oeis.org

1, 1, 1, 1, 7, 15, 25, 37, 100, 229, 454, 811, 1732, 3777, 7858, 15339, 31273, 65536, 136600, 276535, 562728, 1159942, 2400783, 4918159, 10052140, 20627526, 42480474, 87254743, 178855138, 366854368
Offset: 0

Views

Author

R. J. Mathar, Jan 29 2014

Keywords

Comments

Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.

Links

Crossrefs

Cf. A003269 (4 X n floor), A236579 - A236581.
Column k=4 of A250662.
Cf. A251074.

Programs

  • Maple
    p := (1-x)^3*(x+1)^3*(x^2+1)^3*(x^6-x^4-x^3-x^2+1) ;
q :=  -x^2 -13*x^10 -5*x^18 +8*x^6 -x -x^20 -9*x^4 +16*x^8 -13*x^12 -2*x^19 +1 +10*x^14 +5*x^7 +6*x^15 -6*x^11 +x^22 +6*x^16 +x^17 +2*x^5 -2*x^13 ;
taylor(p/q,x=0,30) ;
gfun[seriestolist](%) ;

Formula

G.f.: p(x)/q(x) with polynomials p and q defined in the Maple code.

A236580 The number of tilings of a 6 X (4n) floor with 1 X 4 tetrominoes.

Original entry on oeis.org

1, 4, 25, 154, 943, 5773, 35344, 216388, 1324801, 8110882, 49657576, 304020556, 1861317163, 11395616227, 69767835259, 427142397547, 2615110919020, 16010597772667, 98022320649478, 600125959188877, 3674175070596919, 22494548423870416, 137719270059617428
Offset: 0

Views

Author

R. J. Mathar, Jan 29 2014

Keywords

Comments

Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.

Links

Crossrefs

Cf. A003269 (4Xn floor), A236579 - A236582.

Programs

  • Maple
    g := (1-x)^3/(-7*x+1+6*x^2-4*x^3+x^4) ;
taylor(%,x=0,30) ;
gfun[seriestolist](%) ;

Formula

G.f.: (1-x)^3/(-7*x+1+6*x^2-4*x^3+x^4).

A236581 The number of tilings of a 7 X (4n) floor with 1 X 4 tetrominoes.

Original entry on oeis.org

1, 5, 37, 269, 1949, 14121, 102313, 741305, 5371097, 38916077, 281964941, 2042966149, 14802232757, 107249008849, 777068573905, 5630220503025, 40793546383409, 295568073335893, 2141527121824885, 15516352499614333, 112423136012925517, 814557513519681785
Offset: 0

Views

Author

R. J. Mathar, Jan 29 2014

Keywords

Comments

Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.

Links

Crossrefs

Cf. A003269 (4Xn floor), A236579 - A236582.

Programs

  • Maple
    g := (1-x)^3/(-8*x+1+6*x^2-4*x^3+x^4) ;
taylor(%,x=0,30) ;
gfun[seriestolist](%) ;
  • Mathematica
    LinearRecurrence[{8, -6, 4, -1}, {1, 5, 37, 269}, 19] (* Jean-François Alcover, Feb 19 2019 *)

Formula

G.f.: (1-x)^3/(-8*x+1+6*x^2-4*x^3+x^4).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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