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 1-4 of 4 results.

A172231 Number of ways to place 5 nonattacking wazirs on a 5 X n board.

Original entry on oeis.org

0, 2, 174, 1998, 10741, 38438, 107004, 251354, 522528, 990816, 1748883, 2914894, 4635639, 7089658, 10490366, 15089178, 21178634, 29095524, 39224013, 51998766
Offset: 1

Views

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

Comments

Wazir is a (fairy chess) leaper [0,1].

Links

Crossrefs

Cf. A172228, A172229, A172230, A061991.

Programs

  • Mathematica
    CoefficientList[Series[x (5 x^7 + 8 x^6 + 129 x^5 + 512 x^4 + 1323 x^3 + 984 x^2 + 162 x + 2) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = (625*n^5-5750*n^4+23535*n^3-54202*n^2+70640*n-41616)/24, n>=4.
G.f.: x^2*(5*x^7+8*x^6+129*x^5+512*x^4+1323*x^3+984*x^2+162*x+2)/(x-1)^6. - Vaclav Kotesovec, Mar 25 2010

A172232 Number of ways to place 6 nonattacking wazirs on a 6 X n board.

Original entry on oeis.org

0, 2, 504, 10010, 78052, 368868, 1280832, 3612344, 8774380, 19049692, 37898664, 70311824, 123209012, 205885204, 330502992, 512631720, 771833276, 1132294540, 1623506488, 2280989952, 3147068036, 4271685188, 5713272928, 7539662232, 9829042572, 12670967612
Offset: 1

Views

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

Comments

Wazir is a (fairy chess) leaper [0,1].

Links

Crossrefs

Cf. A172229, A172230, A172231, A061992.

Programs

  • Mathematica
    CoefficientList[Series[- 2 x (3 x^9 - 5 x^8 + 100 x^7 + 354 x^6 + 2548 x^5 + 7572 x^4 + 9248 x^3 + 3262 x^2 + 245 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = 2*(486*n^6 -5670*n^5 +30240*n^4 -95230*n^3 +187899*n^2 -220775*n +120540) / 15, n>=5.
G.f.: -2*x^2 * (3*x^9 -5*x^8 +100*x^7 +354*x^6 +2548*x^5 +7572*x^4 +9248*x^3 +3262*x^2 +245*x +1) / (x-1)^7. - Vaclav Kotesovec, Mar 25 2010

A172234 Number of ways to place 7 nonattacking wazirs on a 7 X n board.

Original entry on oeis.org

0, 2, 1478, 50726, 573797, 3581924, 15516804, 52550366, 149162199, 370817854, 831571604, 1717417198, 3316210152, 6054985120, 10545491888, 17638773534, 28489610297, 44631652698, 68064067456, 101350519742, 147731315314, 211249526076, 296891922604, 410745537182
Offset: 1

Views

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

Comments

Wazir is a (fairy chess) leaper [0,1].

Links

Crossrefs

Cf. A172229, A172230, A172231, A172232, A061993.

Programs

  • Mathematica
    CoefficientList[Series[x (7 x^11 - 48 x^10 + 370 x^9 + 40 x^8 + 8541 x^7 + 45282 x^6 + 190420 x^5 + 329248 x^4 + 209261 x^3 + 38958 x^2 + 1462 x+2) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

Formula

a(n) = (117649*n^7-1663893*n^6+10942729*n^5-43685355*n^4+114945646*n^3-199980312*n^2+213228096*n-107390880)/720, n>=6.
For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (k-1)(5k-2)/2/k!*(kn)^(k-1) + ...
G.f.: x^2*(7*x^11-48*x^10+370*x^9+40*x^8+8541*x^7+45282*x^6+190420*x^5 +329248*x^4+209261*x^3+38958*x^2+1462*x+2)/(x-1)^8. - Vaclav Kotesovec, Mar 25 2010

Extensions

More terms from Vincenzo Librandi, May 29 2013

A178410 Number of ways to place 8 nonattacking wazirs on an 8 X n board.

Original entry on oeis.org

0, 2, 4374, 259289, 4255370, 35093344, 189681689, 771464278, 2559099153, 7285273805, 18416621598, 42342480425, 90097012004, 179755977430, 339666241815, 612682858064, 1061605357051, 1776021648675, 2880784715492
Offset: 1

Views

Author

Vaclav Kotesovec, May 27 2010

Keywords

Comments

Wazir is a (fairy chess) leaper [0,1].

Links

Crossrefs

Cf. A172229, A172230, A172231, A172232, A172234.

Programs

  • Mathematica
    CoefficientList[Series[- x (8 x^13 - 112 x^12 + 870 x^11 - 2812 x^10 + 15019 x^9 + 41114 x^8 + 494109 x^7 + 2357839 x^6 + 5805509 x^5 + 5762254 x^4 + 2079065 x^3 + 219995 x^2 + 4356 x + 2) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Formula

a(n) = (1048576*n^8 -17432576*n^7 +136349696*n^6 -658958720*n^5 +2161896569*n^4 -4945969574*n^3 +7719028159*n^2 -7516702410*n +3494080800) / 2520, n >= 7.
G.f.: -x^2 * (8*x^13 -112*x^12 +870*x^11 -2812*x^10 +15019*x^9 +41114*x^8 +494109*x^7 +2357839*x^6 +5805509*x^5 +5762254*x^4 +2079065*x^3 +219995*x^2 +4356*x +2) / (x-1)^9.
Showing 1-4 of 4 results.

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