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%I #49 Mar 18 2024 19:48:49
%S 1,9,41,129,321,625,997,1413,1885,2425,3033,3709,4453,5265,6145,7093,
%T 8109,9193,10345,11565,12853,14209,15633,17125,18685,20313,22009,
%U 23773,25605,27505,29473,31509,33613,35785,38025,40333,42709,45153,47665,50245,52893
%N The number of distinct positions on an infinite chessboard reachable by the (2,3)-leaper in <= n moves.
%H Colin Barker, <a href="/A297740/b297740.txt">Table of n, a(n) for n = 0..1000</a>
%H R. J. Mathar, <a href="/A297740/a297740_1.pdf">Fairy chess leaper minimum moves on the infinite chessboard</a>, (2018).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 34*n^2 + 30*n + 9 for n >= 6.
%F From _Colin Barker_, Jan 05 2018: (Start)
%F G.f.: (1 + x)*(1 + 5*x + 12*x^2 + 20*x^3 + 28*x^4 - 20*x^5 - 24*x^6 + 12*x^8) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9. (End)
%t LinearRecurrence[{3, -3, 1}, {1, 9, 41, 129, 321, 625, 997, 1413, 1885, 2425}, 50] (* _Paolo Xausa_, Mar 17 2024 *)
%o (PARI) Vec((1 + x)*(1 + 5*x + 12*x^2 + 20*x^3 + 28*x^4 - 20*x^5 - 24*x^6 + 12*x^8) / (1 - x)^3 + O(x^40)) \\ _Colin Barker_, Jan 07 2018
%Y Cf. A018836 (1,2)-leaper or (1,3)-leaper, A297741 (3,4)-leaper.
%Y Partial sums of A018839.
%Y Cf. A253974, A254129, A254459.
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Jan 05 2018
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