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.
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
KEYWORD
nonn,easy
AUTHOR
Kival Ngaokrajang, Sep 13 2013
EXTENSIONS
More terms from Colin Barker, Oct 08 2013
STATUS
approved