A230267 Coins left after packing 5 curves coins patterns into fountain of coins base n.

1, 3, 2, 6, 7, 9, 12, 16, 17, 23, 26, 30, 35, 41, 44, 52, 57, 63, 70, 78, 83, 93, 100, 108, 117, 127, 134, 146, 155, 165, 176, 188, 197, 211, 222, 234, 247, 261, 272, 288, 301, 315, 330, 346, 359, 377, 392, 408, 425, 443

Offset

1,2

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 5 curves coins patterns consist of a part of circumference and forms continuous area. There is total 13 distinct patterns. I would like to call "5C4S" type as it cover 4 coins and symmetry. When packing 5C4S into fountain of coins base n, the total number of 5C4S is A001399, the coins left is a(n) and void is A230276. See illustration in links.

Links

Table of n, a(n) for n=1..50.

Kival Ngaokrajang, Illustration of initial terms (U)

Formula

G.f.: x*(x^3 - 2*x^2 + 2*x + 1)/((1-x)*(1-x^2)*(1-x^3)) (conjectured). - Ralf Stephan, Oct 17 2013

Prog

(Small Basic)
a[1]=1
d[2]=2
For n = 1 To 100
  If n+1 >= 3 Then
    If Math.Remainder(n+1, 3)=math.Remainder(n+1, 6) Then
      d2=1
    Else
      d2=Math.Remainder(n+1, 3)+math.Remainder(n+1, 6)*Math.Power(-1, math.Remainder(n+1, 2))
    EndIf
    d[n+1]=d[n]+d2
  EndIf
  a[n+1]=a[n]+d[n+1]
TextWindow.Write(a[n]+", ")
EndFor

Crossrefs

Cf. A008795 (3-curves coins patterns), A074148, A229093, A229154 (4-curves coins patterns), A001399 (5-curves coins patterns), A229593 (6-curves coins patterns).

Sequence in context: A026187 A026211 A021310 * A286226 A269852 A329691

Adjacent sequences: A230264 A230265 A230266 * A230268 A230269 A230270

Keyword

nonn

Author

Kival Ngaokrajang, Oct 15 2013

Status

approved