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.

A172222 Number of ways to place 4 nonattacking zebras on a 4 X n board.

Original entry on oeis.org

1, 70, 406, 1168, 2948, 6576, 13122, 23808, 40168, 63996, 97344, 142516, 202072, 278828, 375856, 496484, 644296, 823132, 1037088, 1290516, 1588024, 1934476, 2334992, 2794948, 3319976
Offset: 1

Views

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

Comments

Zebra is a (fairy chess) leaper [2,3].

Links

Crossrefs

Cf. A172139, A061990, A172221.

Programs

  • Mathematica
    CoefficientList[Series[-(4 x^12 - 6 x^11 - 2 x^10 - 52 x^9 + 160 x^8 - 88 x^7 + 2 x^6 - 195 x^5 + 473 x^4 - 172 x^3 + 66 x^2 + 65 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = 4*(8*n^4 - 48*n^3 + 202*n^2 - 471*n + 507)/3, n>=9.
G.f.: -x * (4*x^12 -6*x^11 -2*x^10 -52*x^9 +160*x^8 -88*x^7 +2*x^6 -195*x^5 +473*x^4 -172*x^3 +66*x^2 +65*x +1) / (x-1)^5. - Vaclav Kotesovec, Mar 25 2010

A172223 Number of ways to place 5 nonattacking zebras on a 5 X n board.

Original entry on oeis.org

1, 252, 1925, 6534, 20502, 57710, 142312, 308254, 606051, 1105332, 1897899, 3100250, 4857000, 7344010, 10771530, 15387310, 21479725, 29380900, 39469835, 52175530, 67980110, 87421950, 111098800, 139670910, 173864155
Offset: 1

Views

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

Comments

Zebra is a (fairy chess) leaper [2,3].

Links

Crossrefs

Cf. A172140, A061991, A172221, A172222.

Programs

  • Mathematica
    CoefficientList[Series[(14 x^16 - 32 x^15 + 14 x^14 - 292 x^13 + 898 x^12 - 536 x^11 + 514 x^10 - 4232 x^9 + 7258 x^8 - 3296 x^7 + 266 x^6 - 2018 x^5 + 5148 x^4 - 1256 x^3 + 428 x^2 + 246 x+1) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = 5*(125n^5-1250n^4+7575n^3-28426n^2+64000n-67056)/24, n>=12.
G.f.: x * (14*x^16 -32*x^15 +14*x^14 -292*x^13 +898*x^12 -536*x^11 +514*x^10 -4232*x^9 +7258*x^8 -3296*x^7 +266*x^6 -2018*x^5 +5148*x^4 -1256*x^3 +428*x^2 +246*x +1) / (x-1)^6. - Vaclav Kotesovec, Mar 25 2010

A172224 Number of ways to place 6 nonattacking zebras on a 6 X n board.

Original entry on oeis.org

1, 924, 8989, 37270, 145233, 525796, 1605490, 4136952, 9435413, 19632414, 37957424, 69050898, 119351315, 197524064, 314935542, 486171662, 729604121, 1068003424, 1529198580, 2146783422, 2960869583, 4018886128, 5376425842
Offset: 1

Views

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

Comments

Zebra is a (fairy chess) leaper [2,3].

Links

Crossrefs

Cf. A061992, A172221, A172222, A172223.

Programs

  • Mathematica
    CoefficientList[Series[-(32 x^20 - 48 x^19 - 84 x^18 - 1004 x^17 + 3350 x^16 - 802 x^15 + 3364 x^14 - 32132 x^13 + 42540 x^12 + 3538 x^11 + 10674 x^10 - 126767 x^9 + 151663 x^8 - 20769 x^7 - 34421 x^6 + 9539 x^5 + 40807 x^4 - 6284 x^3 + 2542 x^2 + 917 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = (1944n^6-27540n^5+227070n^4-1222555n^3+4366071n^2-9580580n+9925860)/30, n>=15.
For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (k-1)(9k-20)/2/k!*(kn)^(k-1) + ...
G.f.: -x * (32*x^20 -48*x^19 -84*x^18 -1004*x^17 +3350*x^16 -802*x^15 +3364*x^14 -32132*x^13 +42540*x^12 +3538*x^11 +10674*x^10 -126767*x^9 +151663*x^8 -20769*x^7 -34421*x^6 +9539*x^5 +40807*x^4 -6284*x^3 +2542*x^2 +917*x +1) / (x-1)^7. - Vaclav Kotesovec, Mar 25 2010
Showing 1-3 of 3 results.

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