A174249 -id:A174249 - cp's OEIS frontend

A247774 Number of tilings of a 5 X n rectangle using n pentominoes of any but the W shape.

1, 1, 5, 56, 461, 3558, 23966, 178127, 1362597, 10194184, 75684682, 561877016, 4192125848, 31292310312, 233221376211, 1737652233817, 12950437458383, 96538803978663, 719609376905074, 5363567352622148, 39977107204818978, 297975192242698825, 2221015587432193750

Offset: 0

Alois P. Heinz, Sep 23 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..500
Wikipedia, Pentomino

Column k=0 of A247710.

Cf. A174249, A233427.

A247775 Number of tilings of a 5 X n rectangle using n pentominoes of any but the X shape.

Original entry on oeis.org

1, 1, 5, 55, 493, 3930, 27207, 207118, 1622723, 12544364, 95912510, 732066083, 5616480627, 43128778000, 330817187318, 2536012919124, 19443866141395, 149118307026576, 1143608532988558, 8769818352137034, 67250342436670138, 515711365536657077, 3954797365004436075

Offset: 0

Alois P. Heinz, Sep 23 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..500
Wikipedia, Pentomino

Column k=0 of A247711.

Cf. A174249, A233427.

A247776 Number of tilings of a 5 X n rectangle using n pentominoes of any but the Y shape.

Original entry on oeis.org

1, 1, 5, 44, 321, 2404, 14692, 98831, 684729, 4642752, 31650422, 213894450, 1451388234, 9868405649, 66968132029, 454745989239, 3086695784357, 20954497956277, 142275120134328, 965860855067492, 6557295186301572, 44517125016379779, 302224231486908372

Offset: 0

Alois P. Heinz, Sep 23 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..500
Wikipedia, Pentomino

Column k=0 of A247712.

Cf. A174249, A233427.

A247777 Number of tilings of a 5 X n rectangle using n pentominoes of any but the Z shape.

Original entry on oeis.org

1, 1, 5, 52, 451, 3498, 23502, 173611, 1323447, 9920654, 73573634, 545170514, 4060213800, 30266880736, 225316532881, 1676398961171, 12475867876511, 92870049802057, 691310371544378, 5145544200921776, 38298595223058076, 285066094324142481, 2121840794371117780

Offset: 0

Alois P. Heinz, Sep 23 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..500
Wikipedia, Pentomino

Column k=0 of A247713.

Cf. A174249, A233427.

A248102 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes N, Y.

Original entry on oeis.org

1, 0, 0, 18, 24, 238, 842, 4360, 25900, 112178, 613140, 2941170, 14789274, 74895336, 369603312, 1866863986, 9294391952, 46543456838, 233028690018, 1164275409976, 5830080180396, 29149585256266, 145845002931724, 729627382873090, 3649578988919810

Offset: 0

Alois P. Heinz, Oct 01 2014

nonn

			a(3) = 18:
._______._._.        .___._______.        .___._______.
|_. .___| | |        |_. |___. ._|        |_. |___. ._|
| |_| | ._| |        | |_____|_| |        | |_____|_| |
| ._| | |_. |        | |___. ._| |        | |___. |_. |
| | ._|_| |_|        | ._| |_|_. |        | ._| |___| |
|_|_|_______| (*2)   |_|_______|_| (*8)   |_|_______|_| (*8)  .

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Pentomino

Cf. A174249, A233427, A234312, A234931, A247680, A247443.

G.f.: (8*x^15 -52*x^14 -64*x^13 +1087*x^12 -2822*x^11 +2369*x^10 +810*x^9 -2047*x^8 +300*x^7 +122*x^6 +208*x^5 +x^4 +6*x^3 +9*x^2 +2*x -1) / (24*x^15 +4*x^14 -680*x^13 +2673*x^12 -4212*x^11 +2139*x^10 +1574*x^9 -2141*x^8 +456*x^7 -160*x^6 +236*x^5 -11*x^4 +24*x^3 +9*x^2 +2*x -1).

A358933 Number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, Z.

Original entry on oeis.org

1, 0, 0, 0, 2, 0, 2, 2, 4, 2, 10, 8, 14, 18, 36, 34, 66, 88, 136, 170, 292, 382, 578, 818, 1244, 1692, 2576, 3676, 5400, 7654, 11412, 16284, 23852, 34448, 50396, 72472, 106046, 153556, 223458, 323430, 471644, 683046, 993958, 1442138, 2097830, 3042314, 4424880

Offset: 0

Alois P. Heinz, Dec 06 2022

			a(7) = 2:
  ._____________.    ._____________.
  | | ._. | ._. |    | ._. | ._. | |
  | |_| |_|_| |_|    |_| |_|_| |_| |
  |_. |___. |_. |    | ._| .___| ._|
  | |_| | |_| | |    | | |_| | |_| |
  |_____|_____|_|    |_|_____|_____|   .
.

Alois P. Heinz, Table of n, a(n) for n = 0..2000
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, signature (0, 0, 5, 2, 10, -4, -7, -35, -26, -34, 13, 43, 94, 115, 51, 30, -124, -99, -276, -52, -131, 182, 128, 298, 189, 71, -30, -118, -118, -96, -56, -8).

Cf. A174249, A343529, A349187, A352421, A361250.

G.f.: (x-1)*(x^2 +x +1)*(4*x^26 +28*x^25 +44*x^24 +29*x^23 +x^22 -36*x^21 -49*x^20 -45*x^19 -61*x^18 +15*x^17 -7*x^16 +60*x^15 +x^14 +59*x^13 -11*x^12 +10*x^11 -37*x^10 -25*x^8 +x^7 -2*x^6 +10*x^5 +4*x^3 -1) / (8*x^32 +56*x^31 +96*x^30 +118*x^29 +118*x^28 +30*x^27 -71*x^26 -189*x^25 -298*x^24 -128*x^23 -182*x^22 +131*x^21 +52*x^20 +276*x^19 +99*x^18 +124*x^17 -30*x^16 -51*x^15 -115*x^14 -94*x^13 -43*x^12 -13*x^11 +34*x^10 +26*x^9 +35*x^8 +7*x^7 +4*x^6 -10*x^5 -2*x^4 -5*x^3 +1).

A366324 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, W, Y, X.

Original entry on oeis.org

1, 0, 0, 0, 2, 2, 8, 0, 22, 40, 134, 100, 266, 448, 1610, 2454, 4806, 7064, 19774, 38320, 81174, 128604, 277540, 553762, 1222204, 2210510, 4352240, 8339138, 17869740, 34938578, 69204722, 131277114, 267512514, 533554754, 1074570418, 2076822340, 4120024394

Offset: 0

Alois P. Heinz, Nov 14 2023

Alois P. Heinz, Table of n, a(n) for n = 0..3367
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 5, 9, 6, -5, 5, 8, 48, -13, -37, -36, 58, 37, -37, -94, 8, 56, 188, -254, -181, 92, -55, 155, -267, -346, 91, 444, -61, 56, -258, 36, 371, 116, -122, -94, 40, 116, 64, 0, 16, 0, 32).

Cf. A174249, A361250, A372221.

G.f.: (16*x^42 +32*x^41 +16*x^40 +20*x^39 +8*x^38 +4*x^37 -40*x^36 +8*x^35 +13*x^34 -42*x^33 -84*x^32 +4*x^31 -79*x^30 +82*x^29 +61*x^28 -50*x^27 -33*x^26 +47*x^25 +21*x^24 +36*x^23 -23*x^22 -102*x^21 +16*x^20 +26*x^19 +12*x^18 -14*x^17 -5*x^16 +x^15 +28*x^14 -11*x^12 +x^11 +6*x^10 -4*x^9 +x^8 -3*x^7 +7*x^5 +3*x^4 +x^2 -1) / (32*x^44 +16*x^42 +64*x^40 +116*x^39 +40*x^38 -94*x^37 -122*x^36 +116*x^35 +371*x^34 +36*x^33 -258*x^32 +56*x^31 -61*x^30 +444*x^29 +91*x^28 -346*x^27 -267*x^26 +155*x^25 -55*x^24 +92*x^23 -181*x^22 -254*x^21 +188*x^20 +56*x^19 +8*x^18 -94*x^17 -37*x^16 +37*x^15 +58*x^14 -36*x^13 -37*x^12 -13*x^11 +48*x^10 +8*x^9 +5*x^8 -5*x^7 +6*x^6 +9*x^5 +5*x^4 +x^2 -1).

A372221 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, W, I, X.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 6, 9, 12, 16, 21, 41, 66, 106, 156, 219, 364, 558, 930, 1444, 2191, 3515, 5361, 8737, 13661, 21478, 34397, 53528, 86137, 135294, 215432, 345081, 546705, 879212, 1395476, 2239086, 3596427, 5767656, 9312008, 14949738, 24163742, 39045229

Offset: 0

Alois P. Heinz, Apr 22 2024

			a(7) = 6:
   ._____________.   ._____________.   ._____________.
   | |_________| |   | | | | | | | |   |_________| | |
   | .___| |___. |   | | | | | | | |   |_________| | |
   |_| ._| |_. |_|   | | | | | | | |   |_________| | |
   | ._|_____|_. |   | | | | | | | |   |_________| | |
   |_|_________|_|   |_|_|_|_|_|_|_|   |_________|_|_|
   ._____________.   ._____________.   ._____________.
   | |_________| |   | |_________| |   | | |_________|
   |_. |_. ._| ._|   | |_________| |   | | |_________|
   | |___| |___| |   | |_________| |   | | |_________|
   | .___|_|___. |   | |_________| |   | | |_________|
   |_|_________|_|   |_|_________|_|   |_|_|_________| .

Alois P. Heinz, Table of n, a(n) for n = 0..4472
Alois P. Heinz, G.f. for A372221
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, order 139.

Cf. A003520, A174249, A366324.

A247118 Number of tilings of a 10 X n rectangle using 2n pentominoes of shape Y.

Original entry on oeis.org

1, 0, 0, 0, 0, 10, 0, 0, 0, 0, 350, 0, 0, 0, 296, 8954, 50, 0, 0, 13516, 242820, 2760, 0, 5832, 602980, 6591140, 126088, 496, 442978, 22506998, 179340480, 4843754, 147924, 24885442, 789989882, 4891089138, 172488058, 13913138, 1184576462, 26387065880

Offset: 0

Alois P. Heinz, Nov 19 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..100
Wikipedia, Pentomino

Cf. A174249, A233427.

A247119 Number of tilings of a 10 X n rectangle using 2n pentominoes of shape P.

Original entry on oeis.org

1, 0, 4, 0, 52, 194, 808, 2858, 13998, 66154, 378268, 1550370, 7987672, 37394810, 190191026, 958595712, 4634180280, 23153016922, 114436235324, 570764742248, 2855728422214, 14134719577328, 70532689287114, 350910293711340, 1748728132235334, 8722708834873854

Offset: 0

Alois P. Heinz, Nov 19 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..800
Wikipedia, Pentomino

Cf. A174249, A233427.

cp's OEIS Frontend

A247774 Number of tilings of a 5 X n rectangle using n pentominoes of any but the W shape.

Views

Author

Keywords

Links

Crossrefs

A247775 Number of tilings of a 5 X n rectangle using n pentominoes of any but the X shape.

Views

Author

Keywords

Links

Crossrefs

A247776 Number of tilings of a 5 X n rectangle using n pentominoes of any but the Y shape.

Views

Author

Keywords

Links

Crossrefs

A247777 Number of tilings of a 5 X n rectangle using n pentominoes of any but the Z shape.

Views

Author

Keywords

Links

Crossrefs

A248102 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes N, Y.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A358933 Number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, Z.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A366324 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, W, Y, X.

Views

Author

Keywords

Links

Crossrefs

Formula

A372221 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, W, I, X.

Views

Author

Keywords

Examples

Links

Crossrefs

A247118 Number of tilings of a 10 X n rectangle using 2n pentominoes of shape Y.

Views

Author

Keywords

Links

Crossrefs

A247119 Number of tilings of a 10 X n rectangle using 2n pentominoes of shape P.

Views

Author

Keywords

Links

Crossrefs