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 1-7 of 7 results.

A201861 Number of ways to place n nonattacking ferses on an n X n board.

Original entry on oeis.org

1, 4, 38, 661, 16286, 527654, 21191208, 1015335608, 56484795166, 3576188894116, 253756155257774, 19937566770720487, 1717714713900798962, 160977153444563000938, 16300053518916522372836, 1773133639291617644092637, 206197950879511078156507433
Offset: 1

Views

Author

Vaclav Kotesovec, Dec 06 2011

Keywords

Comments

Fers is a leaper [1,1].

Links

Crossrefs

Cf. A201243 - A201248, A002465, A067965.

Formula

Asymptotic (Kotesovec, 2011): a(n) ~ n^(2n)/n!*exp(-5/2).

Extensions

a(15) from Vaclav Kotesovec, Jan 03 2012
a(16) from Vaclav Kotesovec, Aug 31 2016
a(17) from Vaclav Kotesovec, May 30 2021

A201243 Number of ways to place 2 non-attacking ferses on an n X n board.

Original entry on oeis.org

0, 4, 28, 102, 268, 580, 1104, 1918, 3112, 4788, 7060, 10054, 13908, 18772, 24808, 32190, 41104, 51748, 64332, 79078, 96220, 116004, 138688, 164542, 193848, 226900, 264004, 305478, 351652, 402868, 459480, 521854, 590368, 665412, 747388, 836710, 933804, 1039108
Offset: 1

Views

Author

Vaclav Kotesovec, Nov 28 2011

Keywords

Comments

Fers is a leaper [1,1].

Links

Crossrefs

Cf. A172123, A201244, A201245, A201246, A201247, A201248.

Programs

  • Magma
    I:=[0, 4, 28, 102, 268]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Apr 30 2013
  • Magma
    [(n-1)*(n^3+n^2-4*n+4)/2: n in [1..40]]; // Vincenzo Librandi, Apr 30 2013
  • Mathematica
    Table[(n - 1) (n^3 + n^2 - 4 n + 4) / 2, {n, 100}] (* Vincenzo Librandi, Apr 30 2013 *)
LinearRecurrence[{5,-10,10,-5,1},{0,4,28,102,268},40] (* Harvey P. Dale, Dec 31 2014 *)

Formula

a(n) = 1/2*(n-1)*(n^3 + n^2 - 4n + 4) by C. Poisson, 1990.
G.f.: 2x^2*(x+1)*(x^2-2x-2)/(x-1)^5.
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Vincenzo Librandi, Apr 30 2013

A201244 Number of ways to place 3 non-attacking ferses on an n X n board.

Original entry on oeis.org

0, 0, 38, 340, 1630, 5552, 15210, 35828, 75530, 146240, 264702, 453620, 742918, 1171120, 1786850, 2650452, 3835730, 5431808, 7545110, 10301460, 13848302, 18357040, 24025498, 31080500, 39780570, 50418752, 63325550, 78871988, 97472790, 119589680, 145734802
Offset: 1

Views

Author

Vaclav Kotesovec, Nov 28 2011

Keywords

Comments

Fers is a leaper [1,1].

Links

Crossrefs

Cf. A172124, A201243, A201245, A201246, A201247, A201248.

Programs

  • Magma
    I:=[0, 0, 38, 340, 1630, 5552, 15210, 35828]; [n le 8 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..40]]; // Vincenzo Librandi, Apr 30 2013
  • Magma
    [0] cat [(n-2)*(n^5+2*n^4-11*n^3 +2*n^2+54*n-60)/6: n in [2..35]]; // Vincenzo Librandi, Apr 30 2013
  • Mathematica
    CoefficientList[Series[- 2 x^2 (x^5 + 3 x^4 - 24 x^3 + 24 x^2 + 37 x + 19) / (x-1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Formula

a(n) = (n-2)*(n^5 + 2n^4 - 11n^3 + 2n^2 + 54n - 60)/6, n>=2.
G.f.: -2x^3*(x^5 + 3x^4 - 24x^3 + 24x^2 + 37x + 19)/(x-1)^7.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Vincenzo Librandi, Apr 30 2013

A201245 Number of ways to place 4 non-attacking ferses on an n X n board.

Original entry on oeis.org

0, 0, 29, 661, 6285, 35378, 143787, 468529, 1301351, 3202970, 7170593, 14872997, 28969129, 53527866, 94568255, 160741233, 264175507, 421511954, 655152581, 994751765, 1478979173, 2157585442, 3093803379, 4367119121, 6076449375, 8343762538, 11318183177
Offset: 1

Views

Author

Vaclav Kotesovec, Nov 28 2011

Keywords

Comments

Fers is a leaper [1,1].

Links

Crossrefs

Cf. A172127, A201243, A201244, A201246, A201247, A201248.

Programs

  • Mathematica
    CoefficientList[Series[- x^2 (2 x^8 - 55 x^7 + 230 x^6 - 254 x^5 - 225 x^4 + 173 x^3 + 1380 x^2 + 400 x + 29)/(x-1)^9, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Formula

a(n) = (n^8 - 30n^6 + 48n^5 + 299n^4 - 912n^3 - 462n^2 + 4368n - 4200)/24, n>=3.
G.f.: -x^3*(2*x^8 - 55*x^7 + 230*x^6 - 254*x^5 - 225*x^4 + 173*x^3 + 1380*x^2 + 400*x + 29)/(x-1)^9.

A201246 Number of ways to place 5 non-attacking ferses on an n X n board.

Original entry on oeis.org

0, 0, 12, 780, 16286, 159452, 992412, 4567836, 16959488, 53617596, 149618794, 377841356, 879314442, 1911495356, 3922051616, 7657895196, 14321764860, 25791609308, 44921419134, 75946019596, 125016699158, 200899440924, 315872975684, 486869916572, 736910896536
Offset: 1

Views

Author

Vaclav Kotesovec, Nov 28 2011

Keywords

Comments

Fers is a leaper [1,1].

Links

Crossrefs

Cf. A172129, A201243, A201244, A201245, A201247, A201248.

Programs

  • Mathematica
    CoefficientList[Series[2 x^2 (11 x^11 - 135 x^10 + 549 x^9 - 993 x^8 + 1172 x^7 - 2968 x^6 + 7085 x^5 - 4715x^4 - 10613 x^3 - 4183 x^2- 324 x - 6)/(x-1)^11, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Formula

a(n) = n^10/120 - 5n^8/12 + 2n^7/3 + 191n^6/24 - 24n^5 - 661n^4/12 + 880n^3/3 - 937n^2/15 - 1176n + 1436, n>=4.
G.f.: 2x^3*(11x^11 - 135x^10 + 549x^9 - 993x^8 + 1172x^7 - 2968x^6 + 7085x^5 - 4715x^4 - 10613x^3 - 4183x^2 - 324x - 6)/(x-1)^11.

A201247 Number of ways to place 6 non-attacking ferses on an n X n board.

Original entry on oeis.org

0, 0, 2, 552, 29412, 527654, 5196928, 34528698, 173951172, 714042302, 2503447216, 7744201834, 21635290132, 55540293510, 132752090192, 298491879178, 636559136340, 1296099575166, 2533344878048, 4774975629082, 8712052571140, 15436347060646, 26634487077600
Offset: 1

Views

Author

Vaclav Kotesovec, Nov 28 2011

Keywords

Comments

Fers is a leaper [1,1].

Links

Crossrefs

Cf. A176886, A201243, A201244, A201245, A201246, A201248.

Programs

  • Mathematica
    CoefficientList[Series[- 2 x^2 (41 x^14 - 502 x^13 + 2506 x^12 - 7605 x^11 + 18870 x^10 - 41305 x^9 + 60117 x^8 - 21366 x^7 - 73987 x^6 + 52960 x^5 + 237560 x^4 + 93891 x^3 + 11196 x^2 + 263 x + 1)/(x-1)^13, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Formula

a(n) = n^12/720 - 5n^10/48 + n^9/6 + 461n^8/144 - 29n^7/3 - 2147n^6/48 + 1289n^5/6 + 65807n^4/360 - 6356n^3/3 + 9185n^2/6 + 22834n/3 - 11478, n>=5.
G.f.: -2x^3*(41x^14 - 502x^13 + 2506x^12 - 7605x^11 + 18870x^10 - 41305x^9 + 60117x^8 - 21366x^7 - 73987x^6 + 52960x^5 + 237560x^4 + 93891x^3 + 11196x^2 + 263x + 1)/(x-1)^13.

A278686 Number of non-equivalent ways to place 7 non-attacking ferses on an n X n board.

Original entry on oeis.org

0, 0, 0, 27, 4860, 164423, 2651890, 25981150, 180378380, 971905679, 4316504623, 16457726539, 55463445891, 168782705327, 471407278652, 1223710587908, 2982045310010
Offset: 1

Views

Author

Heinrich Ludwig, Dec 02 2016

Keywords

Comments

A fers is a leaper [1, 1].
Rotations and reflections of placements are not counted. If they are to be counted, see A201248.

Examples

			There are 27 non-equivalent ways to place 7 non-attacking ferses (X) on a 4 X 4 board, rotations and reflections being ignored, e.g., these two:
   XXXX   X.XX
   ....   ....
   XXX.   X.X.
   ....   X.X.

Links

Crossrefs

Cf. A201248, A232567 (2 ferses), A278682 (3 ferses), A278683 (4 ferses), A278684 (5 ferses), A278685 (6 ferses), A278687, A278688.
Showing 1-7 of 7 results.

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