|
%I #16 Oct 12 2018 23:29:28
%S 1,9,41,129,321,681,1289,2121,3081,4121,5233,6445,7777,9233,10813,
%T 12517,14345,16297,18373,20573,22897,25345,27917,30613,33433,36377,
%U 39445,42637,45953,49393,52957,56645,60457,64393,68453,72637,76945,81377,85933,90613,95417
%N The number of distinct positions on an infinite chessboard reachable by the (3,4)-leaper in <= n moves.
%F Conjecture: a(n) = 62*n^2 + 30*n - 55 for n >= 10.
%F Conjectures from _Colin Barker_, Jan 06 2018: (Start)
%F G.f.: (1 + 6*x + 17*x^2 + 32*x^3 + 48*x^4 + 64*x^5 + 80*x^6 - 24*x^7 - 96*x^8 - 48*x^9 - 8*x^10 + 28*x^11 + 20*x^12 + 4*x^13) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>13.
%F (End)
%Y Cf. A018836 (1,2)-leaper or (1,3)-leaper, A297740 (2,3)-leaper.
%K nonn
%O 0,2
%A _R. J. Mathar_, Jan 05 2018
|
