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 1-9 of 9 results.

A226369 Number of tilings of a 5 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 4, 4, 0, 0, 1, 6, 12, 8, 0, 1, 8, 24, 32, 16, 1, 10, 40, 80, 80, 33, 12, 60, 160, 240, 193, 78, 84, 280, 560, 673, 464, 240, 448, 1120, 1793, 1810, 1168, 928, 2016, 4033, 5396, 4788, 3264, 3872, 8065, 13462, 15580, 12840, 10400
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(6) = 2:
._._._._._._.    ._._._._._._.
|     |     |    |   |   |   |
|     |     |    |___|___|___|
|_____|_____|    |     |     |
|   |   |   |    |     |     |
|___|___|___|    |_____|_____|

Links

Crossrefs

Column k=5 of A226206.

Programs

  • Maple
    a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1,
    `if`(i=6, [2, 1, 0$4][j], 0)))^n. <<1, [0$4][], 1>>)[1, 1]:
seq(a(n), n=0..70);

Formula

G.f.: 1/(1-x^5-2*x^6).
a(n) = a(n-5)+2*a(n-6) for n>5, a(0) = a(5) = 1, a(1) = a(2) = a(3) = a(4) = 0.

A226370 Number of tilings of a 6 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 1, 1, 3, 2, 7, 7, 16, 19, 40, 51, 98, 136, 245, 355, 617, 923, 1560, 2386, 3962, 6147, 10085, 15804, 25716, 40569, 65652, 104040, 167738, 266634, 428798, 683021, 1096560, 1749127, 2804915, 4478363, 7175960, 11464553, 18360713, 29346366, 46982101
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(4) = 3:
._._._._.   ._._._._.   ._._._._.
|       |   |   |   |   |   |   |
|       |   |___|___|   |___|___|
|       |   |       |   |   |   |
|_______|   |       |   |___|___|
|   |   |   |       |   |   |   |
|___|___|   |_______|   |___|___|

Links

Crossrefs

Column k=6 of A226206.

Programs

  • Maple
    a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1,
    `if`(i=6, [1, 0, 2, 1, 1, 0][j], 0)))^n. <<1, 0, 1, 1, 3, 2>>)[1, 1]:
seq(a(n), n=0..60);

Formula

G.f.: 1/(1-x^2-x^3-2*x^4-x^6).
a(n) = a(n-2)+a(n-3)+2*a(n-4)+a(n-6) for n>5, a(0) = a(2) = a(3) = 1, a(1) = 0, a(4) = 3, a(5) = 2.

A226371 Number of tilings of a 7 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 7, 1, 0, 0, 2, 0, 57, 16, 1, 0, 32, 4, 463, 197, 29, 1, 392, 100, 3767, 2150, 518, 46, 4267, 1668, 30763, 21953, 7454, 1128, 43531, 23057, 252755, 215070, 94769, 20728, 426847, 285548, 2094102, 2050219, 1112227, 321677, 4080855, 3290655
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(10) = 2:
._._._._._._._._._._.   ._._._._._._._._._._.
|         |         |   |   |   |   |   |   |
|         |         |   |___|___|___|___|___|
|         |         |   |         |         |
|         |         |   |         |         |
|_________|_________|   |         |         |
|   |   |   |   |   |   |         |         |
|___|___|___|___|___|   |_________|_________|

Links

Crossrefs

Column k=7 of A226206.

Programs

  • Maple
    a:= n-> coeff(series((-x^12-x^9+2*x^6+x^3-1) / (x^19 -x^18 -x^16 -x^15 -2*x^13 -7*x^12 +x^10 -8*x^9 +x^7 +9*x^6 +x^3-1), x, n+1), x, n):
seq(a(n), n=0..70);

Formula

G.f.: (-x^12-x^9+2*x^6+x^3-1) / (x^19 -x^18 -x^16 -x^15 -2*x^13 -7*x^12 +x^10 -8*x^9 +x^7 +9*x^6 +x^3-1).

A226372 Number of tilings of an 8 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 1, 0, 5, 0, 16, 0, 48, 0, 160, 0, 511, 0, 1651, 2, 5341, 4, 17260, 22, 55846, 92, 180658, 322, 584545, 1240, 1891519, 4520, 6120813, 16202, 19807322, 57956, 64098350, 204762, 207430088, 718472, 671273411, 2506702, 2172343071, 8697828, 7030048159
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(4) = 5:
._._._._.  ._._._._.  ._._._._.  ._._._._.  ._._._._.
|       |  |   |   |  |   |   |  |       |  |   |   |
|       |  |___|___|  |___|___|  |       |  |___|___|
|       |  |   |   |  |       |  |       |  |   |   |
|_______|  |___|___|  |       |  |_______|  |___|___|
|       |  |       |  |       |  |   |   |  |   |   |
|       |  |       |  |_______|  |___|___|  |___|___|
|       |  |       |  |   |   |  |   |   |  |   |   |
|_______|  |_______|  |___|___|  |___|___|  |___|___|

Links

Crossrefs

Column k=8 of A226206.

Programs

  • Maple
    a:= n-> coeff(series(-(x-1) *(x+1) *(x^3+x-1) *(x^3+x+1) *(x^11 -x^10 +x^9 -x^8 +x^7 -2*x^6 -x^5 +x^4 -x^3 +x^2 -x+1) / (x^27 -x^26 +5*x^25 -5*x^24 +9*x^23 -8*x^22 +3*x^21 -5*x^20 -18*x^19 +12*x^18 -29*x^17 +29*x^16 -17*x^15 +32*x^14 +16*x^13 -13*x^12 +25*x^11 -28*x^10 +15*x^9 -18*x^8 -4*x^7 +5*x^6 -5*x^5 +5*x^4 -2*x^3 +2*x^2 +x-1), x, n+1), x, n):
seq(a(n), n=0..60);

Formula

G.f.: -(x-1) *(x+1) *(x^3+x-1) *(x^3+x+1) *(x^11 -x^10 +x^9 -x^8 +x^7 -2*x^6 -x^5 +x^4 -x^3 +x^2 -x+1) / (x^27 -x^26 +5*x^25 -5*x^24 +9*x^23 -8*x^22 +3*x^21 -5*x^20 -18*x^19 +12*x^18 -29*x^17 +29*x^16 -17*x^15 +32*x^14 +16*x^13 -13*x^12 +25*x^11 -28*x^10 +15*x^9 -18*x^8 -4*x^7 +5*x^6 -5*x^5 +5*x^4 -2*x^3 +2*x^2 +x-1).

A226373 Number of tilings of a 9 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 19, 0, 0, 50, 17, 0, 499, 34, 2, 1932, 901, 4, 14152, 2904, 455, 66283, 37037, 1319, 420837, 158496, 33772, 2165069, 1414662, 133691, 12858197, 7114650, 1842975, 69205389, 52535381, 8951317, 398719444, 288028604, 88120788, 2192096580
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(14) = 2:
._._._._._._._._._._._._._._.   ._._._._._._._._._._._._._._.
|             |             |   |   |   |   |   |   |   |   |
|             |             |   |___|___|___|___|___|___|___|
|             |             |   |             |             |
|             |             |   |             |             |
|             |             |   |             |             |
|             |             |   |             |             |
|_____________|_____________|   |             |             |
|   |   |   |   |   |   |   |   |             |             |
|___|___|___|___|___|___|___|   |_____________|_____________|

Links

Crossrefs

Column k=9 of A226206.

Programs

  • Maple
    a:= n-> coeff(series(-(6*x^47 -2*x^46 -6*x^45 +14*x^44 -4*x^43 -48*x^42 -7*x^41 +33*x^40 -61*x^39 -13*x^38 +62*x^37 +58*x^36 -20*x^35 -24*x^34 +30*x^33 -61*x^32 +18*x^31 +121*x^30 +86*x^29 -79*x^28 +270*x^27 +123*x^26 -134*x^25 -435*x^24 -113*x^23 +106*x^22 -388*x^21 -83*x^20 +66*x^19 +367*x^18 +60*x^17
-38*x^16 +189*x^15 +22*x^14 -8*x^13 -130*x^12 -13*x^11 +4*x^10 -36*x^9 -2*x^8 +20*x^6 +x^5 +2*x^3 -1) / (2*x^57 -4*x^55 +4*x^54 +2*x^53 -20*x^52 -75*x^51 +28*x^50 +18*x^49 -156*x^48 +89*x^47 +182*x^46 +88*x^45 -129*x^44 +225*x^43 -102*x^42 -53*x^41 -82*x^40 +346*x^39 +176*x^38 -573*x^37 -357*x^36 -242*x^35
+563*x^34 -583*x^33 +460*x^32 -121*x^31 +700*x^30 +8*x^29 +56*x^28 -2274*x^27 -872*x^26 +949*x^25 +1358*x^24 +368*x^23 -530*x^22 +2250*x^21 +394*x^20 -412*x^19 -1366*x^18 -200*x^17 +204*x^16 -694*x^15 -60*x^14 +46*x^13 +386*x^12 +29*x^11 -21*x^10 +79*x^9 +3*x^8 -36*x^6 -x^5 -3*x^3 +1), x, n+1), x, n):
seq(a(n), n=0..50);

Formula

G.f.: see Maple program.

A226374 Number of tilings of a 10 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 1, 0, 8, 1, 40, 2, 160, 17, 796, 104, 3722, 480, 17398, 2687, 82803, 13994, 391543, 71546, 1856274, 370012, 8811898, 1887331, 41818642, 9587496, 198572128, 48548770, 943058746, 244715696, 4479189932, 1229654538, 21277462741, 6160387914, 101081540520
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(7) = 2:
._._._._._._._.   ._._._._._._._.
|   |         |   |         |   |
|___|         |   |         |___|
|   |         |   |         |   |
|___|         |   |         |___|
|   |_________|   |_________|   |
|___|         |   |         |___|
|   |         |   |         |   |
|___|         |   |         |___|
|   |         |   |         |   |
|___|_________|   |_________|___|

Links

Crossrefs

Column k=10 of A226206.

Programs

  • Maple
    # see link for Maple program.

Formula

See link for g.f.

A226375 Number of tilings of an 11 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 0, 0, 0, 4, 51, 0, 0, 0, 104, 777, 3845, 52, 45, 1247, 19600, 96138, 295711, 8256, 27485, 341034, 2741563, 10253987, 22931155, 1312790, 7243470, 60002173, 333466344, 1013398942, 1792951716, 224282542, 1374038796, 8632780685, 37298717355, 95755127099
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(5) = 4:
._._._._._.  ._._._._._.  ._._._._._.  ._._._._._.
|         |  |         |  |   |     |  |     |   |
|         |  |         |  |___|     |  |     |___|
|         |  |         |  |   |_____|  |_____|   |
|         |  |         |  |___|     |  |     |___|
|_________|  |_________|  |   |     |  |     |   |
|   |     |  |     |   |  |___|_____|  |_____|___|
|___|     |  |     |___|  |         |  |         |
|   |_____|  |_____|   |  |         |  |         |
|___|     |  |     |___|  |         |  |         |
|   |     |  |     |   |  |         |  |         |
|___|_____|  |_____|___|  |_________|  |_________|

Links

Crossrefs

Column k=11 of A226206.

A226376 Number of tilings of a 12 X n rectangle using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 1, 1, 13, 4, 98, 57, 511, 499, 3722, 3845, 24823, 31696, 164781, 243930, 1134938, 1847197, 7765162, 13890389, 53540736, 102899049, 371688482, 756873240, 2587867543, 5533483651, 18092417136, 40238855115, 126887317089, 291501063966, 892138812087
Offset: 0

Views

Author

Alois P. Heinz, Jun 05 2013

Keywords

Examples

			a(5) = 4:
._._._._._.  ._._._._._.  ._._._._._.  ._._._._._.
|   |     |  |     |   |  |   |     |  |     |   |
|___|     |  |     |___|  |___|     |  |     |___|
|   |_____|  |_____|   |  |   |_____|  |_____|   |
|___|     |  |     |___|  |___|     |  |     |___|
|   |     |  |     |   |  |   |     |  |     |   |
|___|_____|  |_____|___|  |___|_____|  |_____|___|
|   |     |  |     |   |  |     |   |  |   |     |
|___|     |  |     |___|  |     |___|  |___|     |
|   |_____|  |_____|   |  |_____|   |  |   |_____|
|___|     |  |     |___|  |     |___|  |___|     |
|   |     |  |     |   |  |     |   |  |   |     |
|___|_____|  |_____|___|  |_____|___|  |___|_____|

Links

Crossrefs

Column k=12 of A226206.

A347800 Number of tilings of an n X n square using integer-sided square tiles of area > 1.

Original entry on oeis.org

1, 0, 1, 1, 2, 1, 7, 1, 48, 50, 796, 777, 24823, 9315, 1501873, 2585314, 200614419, 382810931, 52597087873, 48712723680, 27115688491527
Offset: 0

Views

Author

Alois P. Heinz, Sep 14 2021

Keywords

Examples

			a(4) = 2:
  ._._._._.   ._._._._.
  |       |   |   |   |
  |       |   |___|___|
  |       |   |   |   |
  |_______|   |___|___|   .

Crossrefs

Main diagonal of A226206.
Cf. A045846.

Formula

a(n) = A226206(n,n).
Showing 1-9 of 9 results.

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