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A087446
Numbers that are congruent to {1, 6} mod 15.
3
1, 6, 16, 21, 31, 36, 46, 51, 61, 66, 76, 81, 91, 96, 106, 111, 121, 126, 136, 141, 151, 156, 166, 171, 181, 186, 196, 201, 211, 216, 226, 231, 241, 246, 256, 261, 271, 276, 286, 291, 301, 306, 316, 321, 331, 336, 346, 351, 361, 366, 376, 381, 391, 396, 406
OFFSET
1,2
COMMENTS
3*a(n) is conjectured to be the number of edges (bonds) visited when walking around the boundary of a certain equilateral triangle construction at the n-th iteration. See the illustration in the link. Note that isthmus edges (bridges) are counted twice. The pattern is supposed to become the planar Archimedean net 3.12.12 when n -> infinity. - Kival Ngaokrajang, Nov 30 2014
FORMULA
G.f.: x*(1 + 5*x + 9*x^2)/((1 + x)*(1 - x)^2).
E.g.f.: (30*x-1)*exp(x)/4 + 5*exp(-x)/4.
a(n) = (18*n-1)/4 + 5*(-1)^n/4.
a(n) = 15*n - a(n-1) - 23, with a(1)=1. - Vincenzo Librandi, Aug 08 2010
MATHEMATICA
#+{1, 6}&/@(15*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {1, 6, 16}, 60] (* Harvey P. Dale, Dec 05 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Sep 04 2003
EXTENSIONS
Editing: rewording of Kival Ngaokrajang's comment. - Wolfdieter Lang, Dec 06 2014
STATUS
approved