A222308 - OEIS

%I #22 Oct 12 2020 03:12:40

%S 0,6,34,114,285,602,1127,1940,3126,4790,7040,10006,13819,18634,24605,

%T 31912,40732,51270,63726,78330,95305,114906,137379,163004,192050,

%U 224822,261612,302750,348551,399370,455545,517456,585464,659974,741370,830082,926517,1031130,1144351,1266660,1398510,1540406,1692824

%N Let P be a one-move "rider" with move set M={(1,2)}; a(n) is the number of non-attacking positions of two indistinguishable pieces P on an n X n board.

%H S. Chaiken, C. R. H. Hanusa and T. Zaslavsky, <a href="http://people.math.binghamton.edu/zaslav/Tpapers/qqs1.pdf">A q-queens problem I. General theory</a>, preprint, August 7, 2014.

%H S. Chaiken, C. R. H. Hanusa and T. Zaslavsky, <a href="http://people.math.binghamton.edu/zaslav/Tpapers/qqs2.pdf">A q-queens problem II. The square board</a>, preprint, August 7, 2014. See Corollary 5.2.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).

%F a(n) = n^4/2 - 5*n^3/24 - 11*n/48 + (-1)^n*n/16.

%F G.f.: -x^2*(x^4+7*x^3+18*x^2+16*x+6) / ((x-1)^5*(x+1)^2). [_Colin Barker_, Feb 16 2013]

%t LinearRecurrence[{3,-1,-5,5,1,-3,1},{0,6,34,114,285,602,1127},50] (* _Harvey P. Dale_, Mar 09 2016 *)

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Feb 16 2013