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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A265061 Coordination sequence for (2,4,6) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 12, 17, 24, 33, 45, 61, 83, 114, 155, 210, 286, 389, 529, 720, 979, 1331, 1810, 2462, 3349, 4554, 6193, 8423, 11455, 15579, 21188, 28815, 39188, 53296, 72483, 98577, 134064, 182327, 247965, 337232, 458636, 623745, 848292, 1153677, 1569001, 2133841, 2902023, 3946750, 5367579, 7299906, 9927870, 13501901
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^2 + 1) (x^4 + x^2 + 1)/(x^8 - x^7 + x^6 - 2 x^5 + x^4 - 2 x^3 + x^2 - x + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
  • PARI
    Vec((x+1)^2*(x^2+1)*(x^4+x^2+1)/(x^8-x^7+x^6-2*x^5+x^4-2*x^3+x^2-x+1) + O(x^100)) \\ Altug Alkan, Dec 29 2015

Formula

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

A265062 Coordination sequence for (2,4,7) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 12, 17, 25, 36, 50, 70, 98, 137, 193, 271, 379, 531, 744, 1042, 1461, 2048, 2869, 4020, 5633, 7893, 11061, 15500, 21719, 30434, 42646, 59758, 83738, 117340, 164424, 230402, 322855, 452406, 633943, 888325, 1244781, 1744272, 2444193, 3424970, 4799303, 6725112, 9423686, 13205113, 18503907, 25928939, 36333403
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^2 + 1) (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/(x^10 - x^7 - x^6 - x^5 - x^4 - x^3 + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 31 2015 *)
LinearRecurrence[{0,0,1,1,1,1,1,0,0,-1},{1,3,5,8,12,17,25,36,50,70,98},50] (* Harvey P. Dale, May 17 2023 *)
  • PARI
    Vec((x+1)^2*(x^2+1)*(x^6+x^5+x^4+x^3+x^2+x+1)/(x^10-x^7-x^6-x^5-x^4-x^3+1) + O(x^50)) \\ Michel Marcus, Dec 31 2015

Formula

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

A265063 Coordination sequence for (2,4,8) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 12, 17, 25, 37, 53, 75, 107, 152, 216, 309, 441, 628, 895, 1275, 1816, 2588, 3689, 5257, 7491, 10675, 15211, 21675, 30888, 44016, 62723, 89381, 127368, 181499, 258637, 368560, 525200, 748413, 1066493, 1519757, 2165661, 3086079, 4397679, 6266716, 8930104, 12725445, 18133825, 25840796, 36823271, 52473355
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 + 1)*(x^4 + 1)*(x + 1)^2/(x^8 - x^7 - x^5 + x^4 - x^3 - x + 1), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2017 *)
LinearRecurrence[{1,0,1,-1,1,0,1,-1},{1,3,5,8,12,17,25,37,53},50] (* Harvey P. Dale, Jul 26 2024 *)
  • PARI
    Vec((x^2+1)*(x^4+1)*(x+1)^2/(x^8-x^7-x^5+x^4-x^3-x+1) + O(x^100)) \\ Altug Alkan, Dec 29 2015

Formula

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

A265064 Coordination sequence for (2,5,5) tiling of hyperbolic plane.

Original entry on oeis.org

1, 3, 5, 8, 13, 19, 26, 37, 53, 74, 103, 145, 204, 285, 399, 560, 785, 1099, 1540, 2159, 3025, 4238, 5939, 8323, 11662, 16341, 22899, 32088, 44963, 63005, 88288, 123715, 173357, 242920, 340397, 476987, 668386, 936589, 1312413, 1839042, 2576991, 3611057, 5060060, 7090501, 9935695, 13922576, 19509265, 27337715
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^6 - x^4 - x^3 - x^2 + 1), {x, 0, 45}], x] (* Vincenzo Librandi, Jan 20 2016 *)
LinearRecurrence[{0,1,1,1,0,-1},{1,3,5,8,13,19,26},50] (* Harvey P. Dale, Mar 29 2025 *)
  • PARI
    Vec((x^4+x^3+x^2+x+1)*(x+1)^2/(x^6-x^4-x^3-x^2+1) + O(x^50)) \\ Michel Marcus, Jan 20 2016

Formula

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

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
Previous Showing 11-20 of 29 results. Next

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

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