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A229598 Voids left when packing boomerangs into n X n coins. 10
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 (list; graph; refs; listen; history; text; internal format)
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: A323707 A291186 A058055 * A078356 A050093 A120072

Adjacent sequences:  A229595 A229596 A229597 * A229599 A229600 A229601

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Sep 26 2013

STATUS

approved

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Last modified July 14 16:05 EDT 2020. Contains 335729 sequences. (Running on oeis4.)