A201236 -id:A201236 - cp's OEIS frontend

A201237 Number of ways to place 3 non-attacking wazirs on an n X n toroidal board.

0, 0, 6, 208, 1300, 4908, 14112, 34112, 73008, 142700, 259908, 447312, 734812, 1160908, 1774200, 2635008, 3817112, 5409612, 7518908, 10270800, 13812708, 18316012, 23978512, 31027008, 39720000, 50350508, 63249012, 78786512, 97377708, 119484300, 145618408

Offset: 1

Vaclav Kotesovec, Nov 28 2011

nonn

A wazir is a leaper [0,1].

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Cf. A172226, A201236, A201238, A201239, A201240, A201241, A201242.

a(n) = n^2*(n^4-15*n^2+62)/6, n>=4.

G.f.: -2*x^3 * (3*x^7 - 15*x^6 + 25*x^5 - 7*x^4 - 17*x^3 - 15*x^2 + 83*x + 3)/(x-1)^7.

A201238 Number of ways to place 4 non-attacking wazirs on an n X n toroidal board.

Original entry on oeis.org

0, 0, 0, 228, 3850, 27225, 122892, 423152, 1213380, 3046025, 6907890, 14454972, 28330822, 52586065, 93218400, 158854080, 261593552, 418045617, 650576150, 988799100, 1471339170, 2147897257, 3081651412, 4352027760, 6057877500, 8321097785, 11290735962

Offset: 1

Vaclav Kotesovec, Nov 28 2011

Wazir is a leaper [0,1].

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Cf. A172227, A201236, A201237, A201239, A201240, A201241, A201242.

CoefficientList[Series[x^3*(8 x^9 - 54 x^8 + 189 x^7 - 551 x^6 + 1404 x^5 - 2552 x^4 + 2685 x^3 - 783 x^2 - 1798 x - 228)/(x - 1)^9, {x, 0, 20}], x] (* Wesley Ivan Hurt, Jan 19 2017 *)

a(n) = n^2*(n^2-11)*(n^4 - 19n^2 + 114)/24, n>=5.

G.f.: x^4 * (8x^9 - 54x^8 + 189x^7 - 551x^6 + 1404x^5 - 2552x^4 + 2685x^3 - 783x^2 - 1798x - 228)/(x-1)^9.

A201239 Number of ways to place 5 non-attacking wazirs on an n X n toroidal board.

Original entry on oeis.org

0, 0, 0, 128, 6745, 100332, 754453, 3830016, 15038541, 49207020, 140410699, 360001152, 846775007, 1855033964, 3828109545, 7507096576, 14087087961, 25436160108, 44395753647, 75184958080, 123935571963, 199389702380, 313797119069, 484055619840, 733144325125

Offset: 1

Vaclav Kotesovec, Nov 28 2011

nonn

Wazir is a leaper [0,1].

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Cf. A172228, A201236, A201237, A201238, A201240, A201241, A201242.

a(n) = n^2*(n^8 - 50n^6 + 995n^4 - 9370n^2 + 35424)/120, n>=6.

G.f.: -x^4 * (10x^12 - 110x^11 + 685x^10 - 2771x^9 + 6946x^8 - 9350x^7 + 1710x^6 + 15214x^5 - 21392x^4 + 656x^3 + 33177x^2 + 5337x + 128)/(x-1)^11.

A201240 Number of ways to place 6 non-attacking wazirs on an n X n toroidal board.

Original entry on oeis.org

0, 0, 0, 56, 7100, 252792, 3378942, 26249184, 144455454, 625745100, 2271361422, 7192874328, 20427662398, 53065637212, 127956238350, 289628321664, 620834113614, 1269178026012, 2488676915070, 4702895069400, 8598589878606, 15261688799500, 26371002575326

Offset: 1

Vaclav Kotesovec, Nov 28 2011

nonn

Wazir is a leaper [0,1].

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Cf. A178409, A201236, A201237, A201238, A201239, A201241, A201242.

a(n) = n^2*(n^10 - 75*n^8 + 2365*n^6 - 39285*n^4 + 345034*n^2 - 1288680)/720, n>=7.

G.f.: 2*x^4 * (6*x^15 - 103*x^14 + 873*x^13 - 4241*x^12 + 12757*x^11 - 26112*x^10 + 45344*x^9 - 90774*x^8 + 189180*x^7 - 293907*x^6 + 260273*x^5 - 25077*x^4 - 315215*x^3 - 82430*x^2 - 3186*x - 28)/(x-1)^13.

A201241 Number of ways to place 7 non-attacking wazirs on an n X n toroidal board.

Original entry on oeis.org

0, 0, 0, 16, 4450, 442980, 11281312, 139580160, 1103589198, 6433276500, 30047250222, 118507673088, 408912072478, 1265701033492, 3579712962750, 9380986518528, 23027843919870, 53409035159316, 117860600410206, 248890790976000, 505371757001454, 990655558290772

Offset: 1

Vaclav Kotesovec, Nov 28 2011

nonn

Wazir is a leaper [0,1].

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Cf. A201236, A201237, A201238, A201239, A201240, A201242.

a(n) = n^2*(n^12 - 105*n^10 + 4795*n^8 - 122115*n^6 + 1834084*n^4 - 15461460*n^2 + 57441600)/5040, n>=8.

G.f.: -2*x^4 * (7*x^18 - 177*x^17 + 1965*x^16 - 12491*x^15 + 53736*x^14 - 175854*x^13 + 461641*x^12 - 942615*x^11 + 1320318*x^10 - 788656*x^9 - 1206129*x^8 + 3443471*x^7 - 3128600*x^6 - 552570*x^5 + 7435235*x^4 + 2548291*x^3 + 188955*x^2 + 2105*x + 8)/((x-1)^15).

A201242 Number of ways to place 8 non-attacking wazirs on an n X n toroidal board.

Original entry on oeis.org

0, 0, 0, 2, 1550, 546516, 28482279, 585632520, 6829066665, 54504255500, 331490619174, 1642426038486, 6930083422496, 25686190415144, 85541928717375, 260349711114720, 733731834393719, 1934755847570808, 4813391235753128, 11375736647373750, 25684539545337246

Offset: 1

Vaclav Kotesovec, Nov 28 2011

nonn

Wazir is a leaper [0,1].

V. Kotesovec, Non-attacking chess pieces, 6ed, p.402

Cf. A201236, A201237, A201238, A201239, A201240, A201241.

a(n) = n^2*(n^14 - 140n^12 + 8722n^10 - 313880n^8 + 7061089n^6 - 99573740n^4 + 817978188n^2 - 3033601200)/40320, n>=9.

G.f.: x^4 * (16x^21 - 566x^20 + 8182x^19 - 67700x^18 + 377824x^17 - 1531112x^16 + 4601788x^15 - 10205035x^14 + 16637339x^13 - 21628151x^12 + 32135719x^11 - 68863352x^10 + 138461546x^9 - 189569712x^8 + 133644570x^7 + 20663373x^6 - 378949513x^5 - 174710713x^4 - 19400947x^3 - 520438x^2 - 1516x - 2)/(x-1)^17.

A201547 Number of ways to place 9 nonattacking wazirs on an n X n toroidal board.

Original entry on oeis.org

0, 0, 0, 0, 250, 480916, 54916456, 1962132800, 34690541994, 385983794500, 3095143575007, 19437996015280, 100963195651565, 450398154002132, 1773257833600750, 6288010190509312, 20398342362118678, 61282868654684052, 172190699515632837, 456120623076014000

Offset: 1

Vaclav Kotesovec, Dec 02 2011

nonn

Wazir is a leaper [0,1].

V. Kotesovec, Non-attacking chess pieces

Cf. A201236, A201237, A201238, A201239, A201240, A201241, A201242, A201510.

Explicit formula: n^18/362880 - n^16/2016 + 349*n^14/8640 - 467*n^12/240 + 1049629*n^10/17280 - 121049*n^8/96 + 1546301783*n^6/90720 - 346878319*n^4/2520 + 4595485*n^2/9, n>=10.

G.f.: -x^5*(18*x^23 - 854*x^22 + 15942*x^21 - 168082*x^20 + 1174353*x^19 - 5878707*x^18 + 22139332*x^17 - 65539648*x^16 + 159915785*x^15 - 334575275*x^14 + 598795512*x^13 - 842713520*x^12 + 703597341*x^11 + 289921121*x^10 - 2021527454*x^9 + 3166171570*x^8 - 1944444195*x^7 - 501647511*x^6 + 11035282966*x^5 + 6335694166*x^4 + 1000714522*x^3 + 45821802*x^2 + 476166*x + 250)/(x-1)^19.

A201548 Number of ways to place 10 nonattacking wazirs on an n X n toroidal board.

Original entry on oeis.org

0, 0, 0, 0, 10, 308574, 81442802, 5296005568, 146127335256, 2309813476870, 24738873315596, 198759048859008, 1279605298916568, 6906427308782106, 32277449304595350, 133788325435448576, 500896430870051174, 1718268150463137018, 5462521782760829320, 16243031089247644800

Offset: 1

Vaclav Kotesovec, Dec 02 2011

Wazir is a leaper [0,1].

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
V. Kotesovec, Non-attacking chess pieces

Cf. A201236, A201237, A201238, A201239, A201240, A201241, A201242, A201547.

CoefficientList[Series[2 x^4 (10 x^26 - 615 x^25 + 14637 x^24 - 193410 x^23 + 1669110 x^22 - 10270682 x^21 + 47718030 x^20 - 174153546 x^19 + 511148331 x^18 - 1213451007 x^17 + 2302816572 x^16 - 3418379599 x^15 + 4006461091 x^14 - 4626995415 x^13 + 8410419611 x^12 - 19068629603 x^11 + 33871890471 x^10 - 39181017568 x^9 + 18018811352 x^8 - 5120263515 x^7 - 178499919965 x^6 - 123414145507 x^5 - 25801931589 x^4 - 1825246983 x^3 - 37482424 x^2-154182 x - 5) / (x - 1)^21, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 04 2013 *)

Explicit formula: n^20/3628800 - n^18/16128 + 773*n^16/120960 - 761*n^14/1920 + 2820613*n^12/172800 - 356093*n^10/768 + 412940467*n^8/45360 - 2408161207*n^6/20160 + 24029851729*n^4/25200 - 3541971*n^2, n>=11.

G.f.: 2*x^5*(10*x^26 - 615*x^25 + 14637*x^24 - 193410*x^23 + 1669110*x^22 - 10270682*x^21 + 47718030*x^20 - 174153546*x^19 + 511148331*x^18 - 1213451007*x^17 + 2302816572*x^16 - 3418379599*x^15 + 4006461091*x^14 - 4626995415*x^13 + 8410419611*x^12 - 19068629603*x^11 + 33871890471*x^10 - 39181017568*x^9 + 18018811352*x^8 - 5120263515*x^7 - 178499919965*x^6 - 123414145507*x^5 - 25801931589*x^4 - 1825246983*x^3 - 37482424*x^2 - 154182*x - 5)/(x-1)^21.

cp's OEIS Frontend

A201237 Number of ways to place 3 non-attacking wazirs on an n X n toroidal board.

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A201238 Number of ways to place 4 non-attacking wazirs on an n X n toroidal board.

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A201239 Number of ways to place 5 non-attacking wazirs on an n X n toroidal board.

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A201240 Number of ways to place 6 non-attacking wazirs on an n X n toroidal board.

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A201241 Number of ways to place 7 non-attacking wazirs on an n X n toroidal board.

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A201242 Number of ways to place 8 non-attacking wazirs on an n X n toroidal board.

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A201547 Number of ways to place 9 nonattacking wazirs on an n X n toroidal board.

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A201548 Number of ways to place 10 nonattacking wazirs on an n X n toroidal board.

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