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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. MATHEMATICA LinearRecurrence[{1, 1, 1, -1}, {1, 7, 14, 28, 49}, 40] (* Harvey P. Dale, Mar 25 2019 *) 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 25 17:22 EDT 2021. Contains 348255 sequences. (Running on oeis4.)