The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A229093 The clubs patterns appearing in n X n coins. 15
 0, 0, 1, 2, 4, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57, 66, 75, 86, 97, 108, 121, 134, 147, 162, 177, 192, 209, 226, 243, 262, 281, 300, 321, 342, 363, 386, 409, 432, 457, 482, 507, 534, 561, 588, 617, 646, 675, 706, 737, 768, 801, 834, 867, 902, 937, 972, 1009, 1046 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS On the Japanese TV show "Tsuki no Koibito", a girl told her boyfriend that she saw a heart in 4 coins. Actually there are a total of 6 distinct patterns appearing in 2 X 2 coins in which each pattern consists of a part of the perimeter of each coin and forms a continuous area. a(n) is the number of clubs patterns appearing in n X n coins. It is also A008810(n-1), except for the third term. The inverse patterns (stars or voids between clubs) is A030511 (except the second term). See illustration in links. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Kival Ngaokrajang, Illustration for initial terms Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1). FORMULA a(n) = ceiling((n-1)^2/3), a(0) = 0, a(4) = 4. G.f.: x^2*(x^7-2*x^6+x^5-x^4+x^3-x^2-1) / ((x-1)^3*(x^2+x+1)). - Colin Barker, Oct 07 2013 MATHEMATICA CoefficientList[Series[(x^7 - 2 x^6 + x^5 - x^4 + x^3 - x^2 - 1)/((x - 1)^3 (x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 08 2013 *) LinearRecurrence[{2, -1, 1, -2, 1}, {0, 0, 1, 2, 4, 6, 9, 12, 17, 22}, 70] (* Harvey P. Dale, Feb 05 2020 *) PROG (PARI) Vec(x^2*(x^7-2*x^6+x^5-x^4+x^3-x^2-1)/((x-1)^3*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Oct 08 2013 (PARI) a(n) = ceil((n-1)^2/3) \\ Charles R Greathouse IV, Jan 06 2016 CROSSREFS Cf. A008810, A030511, A074148 (heart patterns), A227906, A229154. Sequence in context: A338200 A194450 A080556 * A342371 A064985 A090631 Adjacent sequences: A229090 A229091 A229092 * A229094 A229095 A229096 KEYWORD nonn,easy AUTHOR Kival Ngaokrajang, Sep 13 2013 EXTENSIONS More terms from Colin Barker, Oct 08 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 2 09:28 EST 2024. Contains 370461 sequences. (Running on oeis4.)