A195653 -id:A195653 - cp's OEIS frontend

A195654 Number of ways to place 10n nonattacking kings on a 20 X 2n cylindrical chessboard.

11264, 48132, 251126, 1473764, 9434784, 64923594, 476033636, 3694894500, 30179587994, 257860425672, 2290966142762, 21042965606234, 198765197377402, 1921681775292272, 18940490557328616, 189679152583318596, 1924757095250611458, 19746535064318923758

Offset: 1

Vaclav Kotesovec, Sep 22 2011

nonn

This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 20, number of rows = 2n).

Alex V. Breger, Table of n, a(n) for n = 1..500
Artem M. Karavaev, Zealint blog (in Russian)
V. Kotesovec, Non-attacking chess pieces
Vaclav Kotesovec, Generating function
Index entries for linear recurrences with constant coefficients, order 916.

Cf. A137432, A195653, A195649, A195659.

Recurrence order is 916.

A195648 Number of ways to place 9n nonattacking kings on a 18 x 2n chessboard.

Original entry on oeis.org

5120, 1501674, 144605184, 7683664202, 282359109140, 8080813574550, 193194265398240, 4035559337688370, 75925129079783308, 1314578079936797520, 21279238303065874504, 325878859655043000344, 4765036384361599508980, 67005992305769489072298, 911373843678367079288192

Offset: 1

Vaclav Kotesovec, Sep 22 2011

nonn

Alex V. Breger, Table of n, a(n) for n = 1..1000
Vaclav Kotesovec, Non-attacking chess pieces
Vaclav Kotesovec, Generating function
Index entries for linear recurrences with constant coefficients, order 548.

Column k=9 of A350819.

Cf. A174558, A018807, A195653, A195658.

Recurrence order is 548.

A195655 Number of ways to place 11n nonattacking kings on a 22 X 2n cylindrical chessboard.

Original entry on oeis.org

24576, 106500, 565512, 3392964, 22327496, 158877948, 1212120160, 9849731140, 84719304384, 766319864440, 7241521734020, 71028444904044, 718816489322444, 7466044767879028, 79230397598482712, 855840660674700612, 9381236750764316676, 104090420921618696952

Offset: 1

Vaclav Kotesovec, Sep 22 2011

nonn

This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 22, number of rows = 2n).

Alex V. Breger, Table of n, a(n) for n = 1..500
Artem M. Karavaev, Zealint blog (in Russian)
V. Kotesovec, Non-attacking chess pieces
Max A. Alekseyev, Denominator of the generating function
Vaclav Kotesovec, Generating function
Index entries for linear recurrences with constant coefficients, order 1829.

Cf. A137432, A195653, A195654, A195650, A195660.

Recurrence order is 1829.

A195656 Number of ways to place 12n nonattacking kings on a 24 X 2n cylindrical chessboard.

Original entry on oeis.org

53248, 233476, 1257754, 7682812, 51698178, 378088270, 2980927200, 25173962492, 226268016376, 2149806985106, 21437333168798, 222770819826574, 2396574908171782, 26535227773186536, 300870737118178194, 3479000496509382748, 40885324678195409820

Offset: 1

Vaclav Kotesovec, Sep 22 2011

nonn

This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 24, number of rows = 2n).

Alex V. Breger, Table of n, a(n) for n = 1..500
Max A. Alekseyev, Denominator of the generating function
Artem M. Karavaev, Zealint blog (in Russian)
V. Kotesovec, Non-attacking chess pieces
Vaclav Kotesovec, Generating function
Index entries for linear recurrences with constant coefficients, order 4248.

Cf. A137432, A195653, A195654, A195655, A195651, A195661.

Recurrence order is 4248.

A195658 Number of ways to place 9n nonattacking kings on a vertical cylinder 18 X 2n.

Original entry on oeis.org

1024, 50922, 815816, 7238864, 44693472, 216134044, 877751236, 3130270224, 10105541204, 30179587994, 84719304384, 226268016376, 580363147336, 1440139184616, 3477556916828, 8210011147304, 19021962952188, 43385173057846, 97653259485592, 217359166880016

Offset: 1

Vaclav Kotesovec, Sep 22 2011

nonn

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 18 are in contact (number of columns = 18, number of rows = 2n)

V. Kotesovec, Non-attacking chess pieces
Index entries for linear recurrences with constant coefficients, signature (12, -64, 200, -406, 560, -532, 344, -145, 36, -4).

Cf. A195653, A195648, A137432.

Recurrence: a(n) = -4*a(n-10) + 36*a(n-9) - 145*a(n-8) + 344*a(n-7) - 532*a(n-6) + 560*a(n-5) - 406*a(n-4) + 200*a(n-3) - 64*a(n-2) + 12*a(n-1).
G.f.: (1 + 1012*x + 38698*x^2 + 270088*x^3 + 503686*x^4 + 270112*x^5 + 37900*x^6 + 1516*x^7 + 25*x^8)/((x-1)^8*(2*x-1)^2).
a(n) = (21623809*n - 226349399)*2^n + 8913/40*n^7 + 124781/20*n^6 + 376359/4*n^5 + 977074*n^4 + 294753537/40*n^3 + 787733819/20*n^2 + 135269649*n + 226349400.

cp's OEIS Frontend

A195654 Number of ways to place 10n nonattacking kings on a 20 X 2n cylindrical chessboard.

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A195648 Number of ways to place 9n nonattacking kings on a 18 x 2n chessboard.

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A195655 Number of ways to place 11n nonattacking kings on a 22 X 2n cylindrical chessboard.

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A195656 Number of ways to place 12n nonattacking kings on a 24 X 2n cylindrical chessboard.

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A195658 Number of ways to place 9n nonattacking kings on a vertical cylinder 18 X 2n.

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