

A290398


Number of tiles in distance d from a given heptagon in the truncated order3 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
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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 916
This sequence is important in the game HyperRogue which uses this tiling.
Wikipedia, Truncated order7 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



