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A018841 Number of steps for {2,3} fairy knight to reach (n,n) on infinite chessboard. 1

%I #13 Jan 04 2018 11:42:43

%S 0,2,4,6,4,2,4,6,6,6,4,6,6,6,8,6,8,8,8,10,8,10,10,10,12,10,12,12,12,

%T 14,12,14,14,14,16,14,16,16,16,18,16,18,18,18,20,18,20,20,20,22,20,22,

%U 22,22,24,22,24,24,24,26,24,26,26,26,28,26,28,28,28,30,28,30,30,30,32,30,32,32

%N Number of steps for {2,3} fairy knight to reach (n,n) on infinite chessboard.

%H Colin Barker, <a href="/A018841/b018841.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F For n >= 14, a(n) = a(n-5) + 2. - _David W. Wilson_

%F From _Colin Barker_, Jan 04 2018: (Start)

%F G.f.: 2*x*(1 + x + x^2 - x^3 - x^4 - x^7 + x^8 - x^11 + x^13) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

%F a(n) = a(n-1) + a(n-5) - a(n-6) for n>5.

%F (End)

%o (PARI) concat(0, Vec(2*x*(1 + x + x^2 - x^3 - x^4 - x^7 + x^8 - x^11 + x^13) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ _Colin Barker_, Jan 04 2018

%K nonn,easy

%O 0,2

%A _Marc LeBrun_

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Last modified March 5 03:04 EST 2024. Contains 370537 sequences. (Running on oeis4.)