

A321019


Coordination sequence for 3D tiling (Cairo tiling) X Z, with respect to a 5valent point.


1



1, 5, 16, 36, 63, 98, 143, 196, 255, 322, 399, 484, 575, 674, 783, 900, 1023, 1154, 1295, 1444, 1599, 1762, 1935, 2116, 2303, 2498, 2703, 2916, 3135, 3362, 3599, 3844, 4095, 4354, 4623, 4900, 5183, 5474, 5775, 6084, 6399, 6722, 7055, 7396, 7743, 8098, 8463, 8836, 9215, 9602, 9999
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OFFSET

0,2


COMMENTS

By (Cairo tiling) X Z is meant a stack of layers of the planar Cairo tiling at integer levels.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,4,4,3,1).


FORMULA

G.f.: (x^6x^52*x^44*x^2x1)*(1+x)/((x^2+1)*(x1)^3), which is the product of the g.f.'s for A296368 and A040000.
From Colin Barker, Nov 11 2018: (Start)
a(n) = 3*a(n1)  4*a(n2) + 4*a(n3)  3*a(n4) + a(n5) for n>5.
a(n) = (2 + (i)^(1+n) + i^(1+n) + 8*n^2) / 2 for n>2, where i=sqrt(1).
(End)


PROG

(PARI) Vec((1 + x)*(1 + x + 4*x^2 + 2*x^4 + x^5  x^6) / ((1  x)^3*(1 + x^2)) + O(x^50)) \\ Colin Barker, Nov 11 2018


CROSSREFS

Cf. A040000, A296368.
Sequence in context: A077415 A234362 A108966 * A184635 A328506 A072333
Adjacent sequences: A321016 A321017 A321018 * A321020 A321021 A321022


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Nov 10 2018


STATUS

approved



