

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

Colin Barker, Table of n, a(n) for n = 0..1000
Brian Galebach, kuniform tilings (k <= 6) and their Anumbers
C. GoodmanStrauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, arXiv:1803.08530, March 2018.
Reticular Chemistry Structure Resource (RCSR), The bew tiling (or net)
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.)
Index entries for linear recurrences with constant coefficients, signature (1,1,1).


FORMULA

From Colin Barker, Dec 23 2017: (Start)
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.
Cf. A008574. See A296911 for partial sums.
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.
Sequence in context: A253535 A310601 A310602 * A310603 A310604 A310605
Adjacent sequences: A296907 A296908 A296909 * A296911 A296912 A296913


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 22 2017


STATUS

approved



