

A296910


a(0)=1, a(1)=4; thereafter a(n) = 4*n2*(1)^n.


39



1, 4, 6, 14, 14, 22, 22, 30, 30, 38, 38, 46, 46, 54, 54, 62, 62, 70, 70, 78, 78, 86, 86, 94, 94, 102, 102, 110, 110, 118, 118, 126, 126, 134, 134, 142, 142, 150, 150, 158, 158, 166, 166, 174, 174, 182, 182, 190, 190, 198, 198, 206, 206, 214, 214, 222, 222, 230, 230, 238, 238
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OFFSET

0,2


COMMENTS

Coordination sequence for the bew tiling with respect to a point where two hexagons meet at only a single point. The coordination sequence for the other type of point can be shown to be A008574.
Notes: There is one point on the positive xaxis at edgedistance n from the origin iff n is even; there is one point on the positive yaxis at edgedistance n from the origin iff n>1 is odd; and the number of points inside the first quadrant at distance n from 0 is n if n is odd, and n1 if n is even.
Then a(n) = 2*(number on positive xaxis + number on positive yaxis) + 4*(number in interior of first quadrant).


LINKS

N. J. A. Sloane, Illustration of initial terms. Points in the first quadrant are marked with their edgedistance from the origin (the heavy black circle). (Ignore the black rectangles, which show some fundamental cells for this tiling.)


FORMULA

G.f.: (1 + 3*x + x^2 + 5*x^3  2*x^4) / ((1  x)^2*(1 + x)).
a(n) = a(n1) + a(n2)  a(n3) for n>4.
(End)


MATHEMATICA

{1, 4}~Join~Array[4 #  2 (1)^# &, 59, 2] (* or *)
LinearRecurrence[{1, 1, 1}, {1, 4, 6, 14, 14}, 61] (* or *)
CoefficientList[Series[(1 + 3 x + x^2 + 5 x^3  2 x^4)/((1  x)^2*(1 + x)), {x, 0, 60}], x] (* Michael De Vlieger, Dec 23 2017 *)


PROG

(PARI) Vec((1 + 3*x + x^2 + 5*x^3  2*x^4) / ((1  x)^2*(1 + x)) + O(x^50)) \\ Colin Barker, Dec 23 2017


CROSSREFS

Apart from first two terms, same as A168384.
Coordination sequences for the 20 2uniform tilings in the order in which they appear in the Galebach catalog, together with their names in the RCSR database (two sequences per tiling): #1 krt A265035, A265036; #2 cph A301287, A301289; #3 krm A301291, A301293; #4 krl A301298, A298024; #5 krq A301299, A301301; #6 krs A301674, A301676; #7 krr A301670, A301672; #8 krk A301291, A301293; #9 krn A301678, A301680; #10 krg A301682, A301684; #11 bew A008574, A296910; #12 krh A301686, A301688; #13 krf A301690, A301692; #14 krd A301694, A219529; #15 krc A301708, A301710; #16 usm A301712, A301714; #17 krj A219529, A301697; #18 kre A301716, A301718; #19 krb A301720, A301722; #20 kra A301724, A301726.


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



