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A321019 Coordination sequence for 3-D tiling (Cairo tiling) X Z, with respect to a 5-valent 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 (list; graph; refs; listen; history; text; internal format)
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^6-x^5-2*x^4-4*x^2-x-1)*(1+x)/((x^2+1)*(x-1)^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(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) 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

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Last modified December 4 02:18 EST 2020. Contains 338921 sequences. (Running on oeis4.)