

A230370


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


8



0, 0, 3, 6, 13, 19, 39, 54, 66, 85, 100, 123, 141, 168, 189, 220, 244, 279, 306, 345, 375, 418, 451, 498, 534, 585, 624, 679, 721, 780, 825, 888, 936, 1003, 1054, 1125, 1179, 1254, 1311, 1390, 1450, 1533, 1596, 1683
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OFFSET

1,3


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..44.
Kival Ngaokrajang, Illustration of initial terms (V)


FORMULA

G.f.: x^3*(11*x^8  5*x^7  21*x^6 + 6*x^5 + 9*x^4 + x^2 + 3*x + 3)/((1x)*(1x^2)^2) (conjectured). Ralf Stephan, Oct 19 2013


PROG

(Small Basic)
a[1]=0
a[2]=0
d1[3]=3
For n=1 To 100
If n+2>=4 Then
If Math.Remainder(n+2, 2)=0 Then
d2= 2(n+2)/2
Else
d2= (n+5)/2
EndIf
d1[n+2]=d1[n+1]+d2
EndIf
a[n+2]=a[n+1]+d1[n+2]
TextWindow.Write(a[n]+", ")
EndFor


CROSSREFS

A001399, A230267, A230276 (5curves coins patterns); A074148, A229093, A220154 (4curves coins patterns); A008795 (3curves coins patterns).
Sequence in context: A259583 A064349 A101965 * A285246 A147009 A064290
Adjacent sequences: A230367 A230368 A230369 * A230371 A230372 A230373


KEYWORD

nonn


AUTHOR

Kival Ngaokrajang, Oct 17 2013


STATUS

approved



