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A230370 Voids left after packing 3 curves coins patterns (3c3s type) into fountain of coins base n.

%I A230370 #8 Oct 19 2013 03:19:30
%S A230370 0,0,3,6,13,19,39,54,66,85,100,123,141,168,189,220,244,279,306,345,
%T A230370 375,418,451,498,534,585,624,679,721,780,825,888,936,1003,1054,1125,
%U A230370 1179,1254,1311,1390,1450,1533,1596,1683
%N A230370 Voids left after packing 3 curves coins patterns (3c3s type) into fountain of coins base n.
%C A230370 Refer to arrangement same as A005169: "A fountain is formed by starting with a row of coins, then stacking additional coins on top so that each new coin touches two in the previous row". The 3 curves coins patterns consist of a part of each coin circumference and forms a continuous area. There are total 4 distinct patterns. For selected pattern, I would like to call "3c3s" type as it cover 3 coins and symmetry. When packing 3c3s into fountain of coins base n, the total number of 3c3s is A008805, the coins left is A008795 and voids left is a(n). See illustration in links.
%H A230370 Kival Ngaokrajang, <a href="/A230370/a230370.pdf">Illustration of initial terms (V)</a>
%F A230370 G.f.: x^3*(11*x^8 - 5*x^7 - 21*x^6 + 6*x^5 + 9*x^4 + x^2 + 3*x + 3)/((1-x)*(1-x^2)^2) (conjectured). _Ralf Stephan_, Oct 19 2013
%o A230370 (Small Basic)
%o A230370 a[1]=0
%o A230370 a[2]=0
%o A230370 d1[3]=3
%o A230370 For n=1 To 100
%o A230370   If n+2>=4 Then
%o A230370     If Math.Remainder(n+2,2)=0 Then
%o A230370       d2= 2-(n+2)/2
%o A230370     Else
%o A230370       d2= (n+5)/2
%o A230370     EndIf
%o A230370       d1[n+2]=d1[n+1]+d2
%o A230370   EndIf
%o A230370   a[n+2]=a[n+1]+d1[n+2]
%o A230370   TextWindow.Write(a[n]+", ")
%o A230370 EndFor
%Y A230370 A001399, A230267, A230276 (5-curves coins patterns); A074148, A229093, A220154 (4-curves coins patterns); A008795 (3-curves coins patterns).
%K A230370 nonn
%O A230370 1,3
%A A230370 _Kival Ngaokrajang_, Oct 17 2013