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A087444
Numbers that are congruent to {1, 4} mod 9.
4
1, 4, 10, 13, 19, 22, 28, 31, 37, 40, 46, 49, 55, 58, 64, 67, 73, 76, 82, 85, 91, 94, 100, 103, 109, 112, 118, 121, 127, 130, 136, 139, 145, 148, 154, 157, 163, 166, 172, 175, 181, 184, 190, 193, 199, 202, 208, 211, 217, 220, 226, 229, 235, 238, 244, 247, 253
OFFSET
1,2
COMMENTS
3*a(n) is conjectured to be the total number of sides (straight double bonds (long side) and single bond (short side)) of a certain equilateral triangle expansion shown in one of the links. The pattern is supposed to become the planar Archimedean net 3.3.3.3.6 when n -> infinity. 3*a(n) is also conjectured to be the total number of sided (bonds) in another version of an equilateral triangle expansion that is supposed to become the planar Archimedean net 3.6.3.6. See the illustrations in the links. - Kival Ngaokrajang, Nov 30 2014
FORMULA
G.f.: x*(1+3*x+5*x^2)/((1+x)*(1-x)^2).
E.g.f.: 5 + ((9*x - 17/2)*exp(x) - (3/2)*exp(-x))/2.
a(n) = (18*n - 17 - 3*(-1)^n)/4.
a(n) = 9*n - a(n-1) - 13 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010
MATHEMATICA
Select[Range[300], MemberQ[{1, 4}, Mod[#, 9]]&] (* or *) LinearRecurrence[ {1, 1, -1}, {1, 4, 10}, 60] (* Harvey P. Dale, Jan 22 2019 *)
PROG
(PARI) a(n) = (18*n - 17 - 3*(-1)^n)/4 \\ David Lovler, Aug 20 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 04 2003
EXTENSIONS
Kival Ngaokrajang's comment reworded by Wolfdieter Lang, Dec 05 2014
E.g.f. and formula adapted to offset by David Lovler, Aug 20 2022
STATUS
approved