login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A231065 Voids left after packing X patterns into an of n X n array of coins. 3
1, 0, 5, 8, 9, 16, 17, 24, 29, 36, 41, 48, 53, 60, 65, 76, 85, 92, 101, 108, 121, 132, 141, 152, 161, 176, 189, 200, 213, 224, 241, 256, 269, 284, 297, 316, 333, 348, 365, 380, 401, 420, 437, 456, 473, 496, 517, 536, 557, 576, 601, 624, 645, 668, 689, 716, 741, 764, 789, 812, 841, 868 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

The X pattern (8c5s2 type) is a pattern in which 8 curves cover 5 coins, and is one of a total of 13 such distinct patterns that appear in a tightly-packed 3 X 3 square array of coins of identical size; each of the 8 curves is a circular arc lying along the edge of one of the 5 coins, and the 8 curves are joined end-to-end to form a continuous area.

a(n) is the total number of voids (spaces among coins) left after packing X patterns into an n X n array of coins. The maximum number of X patterns that can be packed into an n X n array of coins is A231056 and coins left is A231064.

a(n) is also the total number of voids left after packing "+" patterns (8c5s1 type) into an n X n array of coins. See illustration in links.

LINKS

Table of n, a(n) for n=2..63.

Kival Ngaokrajang, Illustration of initial terms (V)

FORMULA

Empirical g.f.: x^2*(4*x^16 -8*x^15 +4*x^14 -4*x^13 +8*x^12 -8*x^11 +8*x^10 -4*x^9 +4*x^6 -5*x^5 +2*x^4 +2*x^3 -6*x^2 +2*x -1) / ((x -1)^3*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Nov 27 2013

PROG

(Small Basic)

x[2] = 0

d1[3] = 1

For n = 2 To 100

  If Math.Remainder(n+2, 5) = 1 Then

     d2 = 0

  Else

    If Math.Remainder(n+2, 5) = 4 Then

     d2 = -1

    else

     d2 = 1

    EndIf

  EndIf

  d1[n+2] = d1[n+1] + d2

  x[n+1] = x[n] + d1[n+1]

  If n >= 13 And Math.Remainder(n, 5) = 3 Then

    x[n] = x[n] - 1

  EndIf

  If n=6 or n>=16 And Math.Remainder(n, 5)=1 Then

    x[n] = x[n] + 1

  EndIf

  V = (n-1)*(n-1) - x[n]*4

  TextWindow.Write(V+", ")

EndFor

CROSSREFS

Cf. A008795, A230370 (3-curves); A074148, A227906, A229093, A229154 (4-curves); A001399, A230267, A230276 (5-curves); A229593, A228949, A229598, A002620, A230548, A230549, A230550 (6-curves).

Sequence in context: A334919 A047616 A287551 * A314576 A045221 A046287

Adjacent sequences:  A231062 A231063 A231064 * A231066 A231067 A231068

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Nov 03 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 00:36 EDT 2020. Contains 335762 sequences. (Running on oeis4.)