A229598 Voids left when packing boomerangs into n X n coins.

1, 0, 3, 8, 5, 12, 21, 16, 27, 40, 33, 48, 65, 56, 75, 96, 85, 108, 133, 120, 147, 176, 161, 192, 225, 208, 243, 280, 261, 300, 341, 320, 363, 408, 385, 432, 481, 456, 507, 560, 533, 588, 645, 616, 675, 736, 705, 768

Offset

2,3

Comments

The inverse patterns are voids or stars (consist of 4 perimeter parts of coins) appearing in n X n coins using the same rule as A229593.

Links

Table of n, a(n) for n=2..49.

Kival Ngaokrajang, Illustration of initial terms

Formula

Empirical g.f.: -x^2*(x+1)*(x^4-2*x^3+5*x^2-2*x+1) / ((x-1)^3*(x^2+x+1)^2). - Colin Barker, Oct 06 2013

Example

For n = 2, there is no boomerang can be packed into 2X2 coins, there is 1 void left, a(2) = 1.
For n = 3, there are 2 boomerangs can be packed into 3X3 coins with no void left, a(3) = 0.
...

Prog

(Small Basic)
v[2]=1
d[3]=-1
d[4]=3
d[5]=5
For n=2 To 100
  If n+1 >=6 Then
    If Math.Remainder(n+1, 3)=0 Then
      d[n+1]=d[n-2]-2
    Else
      d[n+1]=d[n-2]+4
    EndIf
  EndIf
  v[n+1]=v[n]+d[n+1]
  TextWindow.Write(v[n]+", ")
EndFor

Crossrefs

Cf. A229093 (Illustration of inverse clubs patterns).

Sequence in context: A291186 A347942 A058055 * A078356 A050093 A120072

Adjacent sequences: A229595 A229596 A229597 * A229599 A229600 A229601

Keyword

nonn

Author

Kival Ngaokrajang, Sep 26 2013

Status

approved