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A061993 Number of ways to place 7 nonattacking queens on a 7 X n board. 7
0, 0, 0, 0, 0, 0, 0, 40, 312, 2038, 9632, 37248, 120104, 335010, 835056, 1897702, 3998456, 7907094, 14818300, 26512942, 45562852, 75580634, 121520020, 190031678, 289879092, 432420154, 632159540, 907376502, 1280833348 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes, part of V. Kotesovec, Between chessboard and computer, 1996, pp. 204 - 206.

FORMULA

Explicit formula (V.Kotesovec, 1992): a(n) = n^7 - 63*n^6 + 1879*n^5 - 34411*n^4 + 417178*n^3 - 3336014*n^2 + 16209916*n - 36693996, n >= 23.

Recurrence: a(n) a(n) = 8*a(n - 1) - 28*a(n - 2) + 56*a(n - 3) - 70*a(n - 4) + 56*a(n - 5) - 28*a(n - 6) + 8*a(n - 7) - a(n - 8), n >= 31.

G.f.: 2*x^7*(510*x^18 - 142*x^17 - 88*x^3 + 1292*x^4 - 1356*x^5 + 2019*x^6 + 264*x^7 - 2857*x^8 + 6472*x^9 - 7616*x^10 + 7462*x^11 - 7831*x^12 + 8326*x^13 - 5672*x^14 + 1998*x^15 - 308*x^16 - 4*x + 331*x^2 + 20 - 140*x^22 + 320*x^21 - 220*x^20 - 284*x^19 + 24*x^23)/(x - 1)^8.

MATHEMATICA

CoefficientList[Series[2 x^7 (510 x^18 - 142 x^17 - 88 x^3 + 1292 x^4 - 1356 x^5 + 2019 x^6 + 264 x^7 - 2857 x^8 + 6472 x^9 - 7616 x^10 + 7462 x^11 - 7831 x^12 + 8326 x^13 - 5672 x^14 + 1998 x^15 - 308 x^16 - 4 x + 331 x^2 + 20 - 140 x^22 + 320 x^21 - 220 x^20 - 284 x^19 + 24 x^23) / (x-1)^8, {x, 0, 40}], x] (* Vincenzo Librandi, May 12 2013 *)

CROSSREFS

Cf. A061989, A061990, A061991, A061992.

Sequence in context: A035099 A065255 A300920 * A087954 A160328 A247407

Adjacent sequences:  A061990 A061991 A061992 * A061994 A061995 A061996

KEYWORD

nonn,easy

AUTHOR

Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 10 2001

STATUS

approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)