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A290398 Number of tiles in distance d from a given heptagon in the truncated order-3 tiling of the heptagonal plane (a.k.a. the "hyperbolic soccerball"). 1
1, 7, 14, 28, 49, 84, 147, 252, 434, 749, 1288, 2219, 3822, 6580, 11333, 19516, 33607, 57876, 99666, 171633, 295568, 508991, 876526, 1509452, 2599401, 4476388, 7708715, 13275052, 22860754, 39368133, 67795224, 116749059, 201051662, 346227812, 596233309 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Eryk Kopczyński, Dorota Celińska and Marek Čtrnáct, HyperRogue: Playing with Hyperbolic Geometry, Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, Pages 9-16

This sequence is important in the game HyperRogue which uses this tiling.

Wikipedia, Truncated order-7 triangular tiling

Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1).

FORMULA

a(n+4) = a(n+3) + a(n+2) + a(n+1) - a(n), for n >= 1. (proved)

G.f.: (1 + 6*x + 6*x^2 + 6*x^3 + x^4) / (1 - x - x^2 - x^3 + x^4). - Colin Barker, Jan 05 2018

EXAMPLE

There is only the original heptagon in distance 0, so a(0)=1. It is adjacent to 7 hexagons, so a(1)=7. These are adjacent to 7 new heptagons and 7 new hexagons, so a(2)=14.

PROG

(PARI) Vec((1 + 6*x + 6*x^2 + 6*x^3 + x^4) / (1 - x - x^2 - x^3 + x^4) + O(x^40)) \\ Colin Barker, Jan 05 2018

CROSSREFS

Sequence in context: A115815 A275241 A071711 * A033895 A196876 A115876

Adjacent sequences:  A290395 A290396 A290397 * A290399 A290400 A290401

KEYWORD

easy,nonn

AUTHOR

Eryk Kopczynski, Jul 29 2017

STATUS

approved

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Last modified October 17 12:50 EDT 2018. Contains 316280 sequences. (Running on oeis4.)