

A227906


Coins left after packing heart patterns (fixed orientation) into n X n coins.


7



2, 4, 4, 9, 6, 13, 8, 17, 10, 21, 12, 25, 14, 29, 16, 33, 18, 37, 20, 41, 22, 45, 24, 49, 26, 53, 28, 57, 30, 61, 32, 65, 34, 69, 36, 73, 38, 77, 40, 81, 42, 85, 44, 89, 46, 93, 48, 97, 50, 101, 52, 105, 54, 109, 56, 113, 58, 117, 60, 121
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OFFSET

2,1


COMMENTS

From a Japanese movie, the girl told her boyfriend that she saw a heart in 4 coins. Actually there are total 6 distinct patterns appearing in 2X2 coins which each pattern consist of a part of circumference of each coin and forms a continuous area.
a(n) is the number of coins left after packing fixed orientation heart patterns (type 4c2s1: 4curve cover 2 coins and symmetry) into n X n coins. The total heart number is A093005 and voids left is A093353. See illustration in links.


LINKS

Table of n, a(n) for n=2..61.
Kival Ngaokrajang, Illustration of initial terms (U)
Index entries for linear recurrences with constant coefficients, signature (0,2,0,1).


FORMULA

From Colin Barker, Oct 30 2013: (Start)
a(n) = (1+(1)^n(3+(1)^n)*n)/2 for n>3.
a(n) = n for n>3 and even.
a(n) = 2*n1 for n>3 and odd.
a(n) = 2*a(n2)a(n4) for n>7.
G.f.: x^2*(x^5x^34*x2) / ((x1)^2*(x+1)^2).(End)


MATHEMATICA

With[{nn=60}, Join[{2, 4}, Riffle[Range[4, nn, 2], Range[9, 2nn+1, 4]]]] (* Harvey P. Dale, Feb 11 2015 *)


PROG

(Small Basic)
For n = 2 To 100
If Math.Remainder(n, 2) = 0 then
a = n
Else
a = a + n
If n = 3 then
a = a  1
endif
EndIf
TextWindow.Write(a+", ")
EndFor
(PARI) Vec(x^2*(x^5x^34*x2)/((x1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Oct 30 2013


CROSSREFS

Cf. A008795, A230370 (3curves), A074148, A229093, A229154 (4curves), A001399, A230267, A230276 (5curves), A229593, A228949, A229598 (6curves).
Sequence in context: A010464 A187209 A006579 * A195727 A256701 A292381
Adjacent sequences: A227903 A227904 A227905 * A227907 A227908 A227909


KEYWORD

nonn,easy


AUTHOR

Kival Ngaokrajang, Oct 19 2013


STATUS

approved



