The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A279442 Number of ways to place 8 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line. 8
 0, 0, 0, 90, 67950, 4531950, 109425330, 1460297160, 13112872920, 88456195800, 480149029800, 2196080372970, 8743233946590, 31033043111070, 99992483914050, 296626638016800, 819218054279520, 2125440234303840, 5218743585428640, 12201529135725450, 27304286810701950 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Column 9 of triangle A279445. Rotations and reflections of placements are counted. LINKS Heinrich Ludwig, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1). FORMULA a(n) = (n^16 -140*n^14 +756*n^13 +2506*n^12 -36540*n^11 +130940*n^10 -117432*n^9 -559615*n^8 +2186100*n^7 -3622360*n^6 +3228876*n^5 -1439892*n^4 +181440*n^3 +45360*n^2)/40320; factorized: a(n) = n^2*(n-1)^2*(n-2)^2*(n-3)^2*(n^8 +12*n^7 -54*n^6 -444*n^5 +1845*n^4 +1392*n^3 -11332*n^2 +9660*n +1260)/8!. a(n) = SUM(1<=j<=17, C(17,j)*(-1)^(j-1)*a(n-j)). G.f.: 90*x^4*(1 +738*x +37656*x^2 +461802*x^3 +1893555*x^4 +2767824*x^5 +1058064*x^6 -331920*x^7 -140913*x^8 +15950*x^9 +3096*x^10 -90*x^11 -3*x^12) / (1 -x)^17. - Colin Barker, Dec 23 2016 MATHEMATICA Table[n^2*(n - 1)^2*(n - 2)^2*(n - 3)^2*(n^8 + 12 n^7 - 54 n^6 - 444 n^5 + 1845 n^4 + 1392 n^3 - 11332 n^2 + 9660 n + 1260)/8!, {n, 21}] (* Michael De Vlieger, Dec 22 2016 *) PROG (PARI) concat(vector(3), Vec(90*x^4*(1 +738*x +37656*x^2 +461802*x^3 +1893555*x^4 +2767824*x^5 +1058064*x^6 -331920*x^7 -140913*x^8 +15950*x^9 +3096*x^10 -90*x^11 -3*x^12) / (1 -x)^17 + O(x^30))) \\ Colin Barker, Dec 23 2016 CROSSREFS Cf. A279444, A279445, A197458. Same problem but 2..7,9 points: A083374, A279437, A279438, A279439, A279440, A279441, A279443. Sequence in context: A134648 A145413 A367459 * A172572 A052277 A172671 Adjacent sequences: A279439 A279440 A279441 * A279443 A279444 A279445 KEYWORD nonn,easy AUTHOR Heinrich Ludwig, Dec 22 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 13 10:15 EDT 2024. Contains 375130 sequences. (Running on oeis4.)