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.

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A265065 Coordination sequence for (2,5,6) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 13, 20, 29, 42, 62, 91, 132, 192, 281, 410, 597, 870, 1269, 1851, 2698, 3933, 5735, 8362, 12191, 17774, 25915, 37784, 55088, 80317, 117102, 170734, 248927, 362932, 529151, 771496, 1124831, 1639989, 2391084, 3486171, 5082793, 7410648, 10804633, 15753020, 22967705, 33486626, 48823082, 71183443, 103784568
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Mathematica
    CoefficientList[Series[(x + 1)^2 (x^4 + x^3 + x^2 + x + 1) (x^4 + x^2 + 1) / (x^10 - x^7 - x^6 - 2 x^5 - x^4 - x^3 + 1), {x, 0, 45}], x] (* Vincenzo Librandi, Jan 20 2016 *)
LinearRecurrence[{0,0,1,1,2,1,1,0,0,-1},{1,3,5,8,13,20,29,42,62,91,132},50] (* Harvey P. Dale, Jun 15 2022 *)
  • PARI
    Vec((x+1)^2*(x^4+x^3+x^2+x+1)*(x^4+x^2+1)/(x^10-x^7-x^6-2*x^5-x^4-x^3+1) + O(x^50)) \\ Michel Marcus, Jan 20 2016

Formula

G.f.: (x+1)^2*(x^4+x^3+x^2+x+1)*(x^4+x^2+1)/(x^10-x^7-x^6-2*x^5-x^4-x^3+1).

A265066 Coordination sequence for (2,5,7) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 13, 20, 30, 45, 67, 100, 149, 221, 329, 491, 731, 1087, 1618, 2409, 3586, 5338, 7946, 11828, 17607, 26209, 39013, 58074, 86448, 128683, 191552, 285138, 424447, 631817, 940501, 1399997, 2083987, 3102151, 4617754, 6873828, 10232143, 15231214, 22672656, 33749729, 50238677, 74783553, 111320204, 165707396
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Mathematica
    CoefficientList[Series[(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) (x^4 + x^3 + x^2 + x + 1) (x + 1)^2 / (x^12 + x^11 - x^9 - 2 x^8 - 3 x^7 - 3 x^6 - 3 x^5 - 2 x^4 - x^3 + x + 1), {x, 0, 45}], x] (* Vincenzo Librandi, Jan 20 2016 *)
  • PARI
    Vec((x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(x+1)^2/(x^12+x^11-x^9-2*x^8-3*x^7-3*x^6-3*x^5-2*x^4-x^3+x+1) + O(x^50)) \\ Michel Marcus, Jan 20 2016

Formula

G.f.: (x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(x+1)^2/(x^12+x^11-x^9-2*x^8-3*x^7-3*x^6-3*x^5-2*x^4-x^3+x+1).

A265067 Coordination sequence for (2,5,8) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 13, 20, 30, 46, 70, 105, 158, 238, 358, 539, 813, 1225, 1844, 2777, 4183, 6300, 9488, 14291, 21525, 32419, 48827, 73540, 110761, 166821, 251256, 378426, 569960, 858437, 1292923, 1947317, 2932923, 4417381, 6653176, 10020585, 15092360, 22731142, 34236184, 51564338, 77662890, 116970850, 176173970, 265341902
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Mathematica
    CoefficientList[Series[(x + 1)^2 (x^4 + x^3 + x^2 + x + 1) (x^6 + x^4 + x^2 + 1) / (x^12 - x^9 - x^8 - 2 x^7 - x^6 - 2 x^5 - x^4 - x^3 + 1), {x, 0, 45}], x] (* Vincenzo Librandi, Jan 20 2016 *)
  • PARI
    Vec((x+1)^2*(x^4+x^3+x^2+x+1)*(x^6+x^4+x^2+1)/(x^12-x^9-x^8-2*x^7-x^6-2*x^5-x^4-x^3+1) + O(x^50)) \\ Michel Marcus, Jan 20 2016

Formula

G.f.: (x+1)^2*(x^4+x^3+x^2+x+1)*(x^6+x^4+x^2+1)/(x^12-x^9-x^8-2*x^7-x^6-2*x^5-x^4-x^3+1).

A265068 Coordination sequence for (2,5,infinity) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 13, 20, 30, 46, 71, 109, 167, 256, 393, 603, 925, 1419, 2177, 3340, 5124, 7861, 12060, 18502, 28385, 43547, 66808, 102494, 157242, 241234, 370091, 567778, 871061, 1336345, 2050164, 3145275, 4825348, 7402845, 11357132, 17423632, 26730600, 41008957, 62914209, 96520321, 148077398, 227174087, 348520885
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Mathematica
    CoefficientList[Series[-(x^4 + x^3 + x^2 + x + 1) (x + 1)^2/(x^5 + x^4 + x^3 + x^2 - 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
  • PARI
    Vec(-(x^4+x^3+x^2+x+1)*(x+1)^2/(x^5+x^4+x^3+x^2-1) + O(x^50)) \\ Michel Marcus, Dec 30 2015

Formula

G.f.: -(x^4+x^3+x^2+x+1)*(x+1)^2/(x^5+x^4+x^3+x^2-1).

A265069 Coordination sequence for (2,6,6) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 13, 21, 32, 47, 71, 108, 163, 245, 368, 555, 837, 1260, 1897, 2857, 4304, 6483, 9763, 14704, 22147, 33357, 50240, 75667, 113965, 171648, 258525, 389373, 586448, 883271, 1330327, 2003652, 3017771, 4545173, 6845648, 10310475, 15528973, 23388740, 35226617, 53056065, 79909632, 120354747, 181270579, 273018088
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Mathematica
    CoefficientList[Series[(x^5 + x^4 + x^3 + x^2 + x + 1) (x + 1)/(x^6 - x^5 - x^3 - x + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
  • PARI
    Vec((x^5+x^4+x^3+x^2+x+1)*(x+1)/(x^6-x^5-x^3-x+1) + O(x^50)) \\ Michel Marcus, Dec 30 2015

Formula

G.f.: (x^5+x^4+x^3+x^2+x+1)*(x+1)/(x^6-x^5-x^3-x+1).

A265070 Coordination sequence for (2,6,infinity) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 13, 21, 33, 51, 80, 126, 198, 311, 488, 766, 1203, 1889, 2966, 4657, 7312, 11481, 18027, 28305, 44443, 69782, 109568, 172038, 270125, 424136, 665956, 1045649, 1641823, 2577904, 4047689, 6355468, 9979021, 15668533, 24601905, 38628615, 60652616, 95233542, 149530690, 234785211, 368647368, 578830674
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Magma
    I:=[1,3,5,8,13,21,33]; [n le 7 select I[n] else Self(n-1)+Self(n-3)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Dec 30 2015
  • Mathematica
    CoefficientList[Series[-(x^5 + x^4 + x^3 + x^2 + x + 1) (x + 1)/(x^5 + x^3 + x - 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
  • PARI
    x='x+O('x^50); Vec((x+1)*(x^5+x^4+x^3+x^2+x+1)/(1-x-x^3-x^5)) \\ G. C. Greubel, Aug 07 2017

Formula

G.f.: -(x^5+x^4+x^3+x^2+x+1)*(x+1)/(x^5+x^3+x-1).
a(n) = a(n-1)+a(n-3)+a(n-5) for n>6. - Vincenzo Librandi, Dec 30 2015

A265071 Coordination sequence for (3,3,4) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 6, 10, 15, 22, 31, 44, 62, 87, 122, 171, 240, 336, 471, 660, 925, 1296, 1816, 2545, 3566, 4997, 7002, 9812, 13749, 19266, 26997, 37830, 53010, 74281, 104088, 145855, 204382, 286394, 401315, 562350, 788003, 1104204, 1547286, 2168163, 3038178, 4257303, 5965624, 8359440, 11713819, 16414204, 23000705, 32230160
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Magma
    I:=[1,3,6,10,15,22,31]; [n le 7 select I[n] else Self(n-2)+Self(n-3)+Self(n-4)- Self(n-6): n in [1..50]]; // Vincenzo Librandi, Dec 30 2015
  • Mathematica
    CoefficientList[Series[(x^3 + x^2 + x + 1) (x^2 + x + 1) (x + 1)/(x^6 - x^4 - x^3 - x^2 + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
  • PARI
    x='x+O('x^50); Vec((x^3+x^2+x+1)*(x^2+x+1)*(x+1)/(x^6-x^4-x^3-x^2+1)) \\ G. C. Greubel, Aug 07 2017

Formula

G.f.: (x^3+x^2+x+1)*(x^2+x+1)*(x+1)/(x^6-x^4-x^3-x^2+1).
a(n) = a(n-2)+a(n-3)+a(n-4)-a(n-6) for n>6. - Vincenzo Librandi, Dec 30 2015

A265072 Coordination sequence for (3,3,5) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 6, 10, 16, 25, 38, 57, 86, 130, 196, 295, 444, 669, 1008, 1518, 2286, 3443, 5186, 7811, 11764, 17718, 26686, 40193, 60536, 91175, 137322, 206826, 311508, 469173, 706638, 1064293, 1602970, 2414290, 3636248, 5476683, 8248628, 12423553, 18711556, 28182142, 42446130, 63929631, 96286698, 145020831, 218421048
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Mathematica
    CoefficientList[Series[(x^2 + x + 1) (x^4 + x^3 + x^2 + x + 1)/(x^6 - x^5 - x^3 - x + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
LinearRecurrence[{1,0,1,0,1,-1},{1,3,6,10,16,25,38},50] (* Harvey P. Dale, Oct 07 2022 *)
  • PARI
    x='x+O('x^50); Vec((x^2+x+1)*(x^4+x^3+x^2+x+1)/(x^6-x^5-x^3-x+1)) \\ G. C. Greubel, Aug 07 2017

Formula

G.f.: (x^2+x+1)*(x^4+x^3+x^2+x+1)/(x^6-x^5-x^3-x+1).

A265073 Coordination sequence for (3,3,6) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 6, 10, 16, 26, 41, 64, 99, 154, 240, 374, 582, 905, 1408, 2191, 3410, 5306, 8256, 12846, 19989, 31104, 48399, 75310, 117184, 182342, 283730, 441493, 686976, 1068955, 1663326, 2588186, 4027296, 6266594, 9751009, 15172864, 23609435, 36736994, 57163872, 88948710, 138406878, 215365281, 335114880, 521448871
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Mathematica
    CoefficientList[Series[(x^3 + 1) (x^2 + x + 1) (x + 1)/(x^6 - x^5 - x^4 + x^3 - x^2 - x + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
  • PARI
    x='x+O('x^50); Vec((x^3+1)*(x^2+x+1)*(x+1)/(x^6-x^5-x^4+x^3-x^2-x+1)) \\ G. C. Greubel, Aug 07 2017

Formula

G.f.: (x^3+1)*(x^2+x+1)*(x+1)/(x^6-x^5-x^4+x^3-x^2-x+1).

A265074 Coordination sequence for (3,3,7) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 6, 10, 16, 26, 42, 67, 106, 167, 264, 418, 662, 1048, 1658, 2623, 4150, 6567, 10392, 16444, 26020, 41172, 65148, 103087, 163120, 258113, 408424, 646268, 1022620, 1618140, 2560460, 4051537, 6410938, 10144329, 16051850, 25399600, 40190986, 63596094, 100631100, 159233337, 251962422, 398692029, 630869210
Offset: 0

Views

Author

N. J. A. Sloane, Dec 29 2015

Keywords

Links

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Programs

  • Magma
    I:=[1,3,6,10,16,26,42,67,106]; [n le 9 select I[n] else Self(n-1)+Self(n-3)+Self(n-5)+Self(n-7)-Self(n-8): n in [1..50]]; // Vincenzo Librandi, Dec 30 2015
  • Mathematica
    CoefficientList[Series[(x^2 + x + 1) (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/(x^8 - x^7 - x^5 - x^3 - x + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
  • PARI
    x='x+O('x^50); Vec((x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)/(x^8-x^7-x^5-x^3-x+1)) \\ G. C. Greubel, Aug 07 2017

Formula

G.f.: (x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)/(x^8-x^7-x^5-x^3-x+1).
a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)-a(n-8) for n>8. - Vincenzo Librandi, Dec 30 2015
Previous Showing 21-30 of 49 results. Next

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

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