A228949 - OEIS

%I #22 Jan 19 2019 13:26:57

%S 4,3,7,13,6,13,22,9,19,31,12,25,40,15,31,49,18,37,58,21,43,67,24,49,

%T 76,27,55,85,30,61,94,33,67,103,36,73,112,39,79,121,42,85,130,45,91,

%U 139,48,97,148,51,103,157,54,109,166,57

%N Coins left when packing boomerangs into n X n coins.

%C The coins left after packing boomerangs into n X n coins using the same rule as A229593. See illustration in links.

%H Kival Ngaokrajang, <a href="/A228949/a228949.pdf">Illustration of initial terms</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).

%F G.f. -x^2*(-4-3*x-7*x^2-5*x^3+x^5) / ( (x-1)^2*(1+x+x^2)^2 ). - _R. J. Mathar_, Oct 16 2013

%t LinearRecurrence[{0,0,2,0,0,-1},{4,3,7,13,6,13},80] (* _Harvey P. Dale_, Jan 19 2019 *)

%o (Small Basic)

%o u[2]=4

%o d[3]=-1

%o d[4]=4

%o d[5]=6

%o For n=2 To 100

%o   If n+1 >=6 Then

%o     If Math.Remainder(n+1,3)=0 Then

%o       d[n+1]=d[n-2]-6

%o     Else

%o       d[n+1]=d[n-2]+3

%o     EndIf

%o   EndIf

%o   u[n+1]=u[n]+d[n+1]

%o   TextWindow.Write(u[n]+", ")

%o EndFor

%Y Cf. A229593 (Boomerangs), A229598 (Voids), A017209 (trisection), A008585 (trisection), A016921 (trisection).

%K nonn,easy

%O 2,1

%A _Kival Ngaokrajang_, Oct 05 2013