OFFSET
0,1
COMMENTS
Numbers m such that 8*m - 103 is a square. - Bruce J. Nicholson, Jul 26 2017
For n>2, a(n+14) is the number of ways to tile an equilateral triangle of side length 2*n+1 with smaller equilateral triangles of side length n and side length 1. For example, with n=3, there are a(17)=166 ways to tile an equilateral triangle of side length 7 with smaller ones of sides 3 and 1, including the one way with 49 triangles of sides 1 and the seven ways with four triangles of sides 3 (and thirteen triangles of sides 1). - Ahmed ElKhatib and Greg Dresden, Sep 02 2024
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = A000217(n) + 13.
From G. C. Greubel, Feb 19 2021: (Start)
G.f.: (13 -25*x +13*x^2)/(1-x)^3.
E.g.f.: (26 +2*x +x^2)*exp(x)/2. (End)
Sum_{n>=0} 1/a(n) = 2*Pi*tanh(sqrt(103)*Pi/2)/sqrt(103). - Amiram Eldar, Dec 13 2022
MAPLE
MATHEMATICA
Table[n*(n+1)/2 +13, {n, 0, 5!}]
PROG
(PARI) a(n)=n*(n+1)/2 + 13 \\ Charles R Greathouse IV, Jun 16 2017
(Sage) [13 + binomial(n+1, 2) for n in (0..60)] # G. C. Greubel, Feb 19 2021
(Magma) [13 + Binomial(n+1, 2): n in [0..60]]; // G. C. Greubel, Feb 19 2021
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Vladimir Joseph Stephan Orlovsky, Feb 07 2010
EXTENSIONS
Title and offset changed by G. C. Greubel, Feb 19 2021
STATUS
approved