A108752 Numbers k such that 12 divides k*(k+1).
0, 3, 8, 11, 12, 15, 20, 23, 24, 27, 32, 35, 36, 39, 44, 47, 48, 51, 56, 59, 60, 63, 68, 71, 72, 75, 80, 83, 84, 87, 92, 95, 96, 99, 104, 107, 108, 111, 116, 119, 120, 123, 128, 131, 132, 135, 140, 143, 144, 147, 152, 155, 156, 159, 164, 167, 168, 171, 176, 179, 180
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..5000
- Robert Phillips, Triangular numbers which are sums of two triangular numbers, 2006.
- Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
Programs
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Magma
[3*n-2-(-1)^((2*n-3-(-1)^n) div 4): n in [1..80]]; // Vincenzo Librandi, May 04 2017
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Maple
a:= proc(n) if is(n*(n+1)/12, integer) then n fi end: seq(a(n), n=0..200); # Emeric Deutsch, Jun 25 2005
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Mathematica
Select[ Range[0, 182], Mod[ #(# + 1), 12] == 0 &] (* Robert G. Wilson v, Jun 25 2005 *) LinearRecurrence[{2, -2, 2, -1}, {0, 3, 8, 11}, 200] (* Vincenzo Librandi, Jun 04 2017 *)
Formula
From R. J. Mathar, Jan 07 2009: (Start)
G.f.: x*(3 + 2*x + x^2)/((1 + x^2)*(1 - x)^2). (End)
a(n) = 3*n - 2 - (-1)^((2*n-3-(-1)^n)/4). - Luce ETIENNE, Apr 04 2015
Sum_{n>=2} 1/a(n) = log(2)/2 + arccoth(sqrt(3))/(2*sqrt(3)) - Pi*(3+2*sqrt(3))/72. - Amiram Eldar, Jul 26 2024
Extensions
More terms from Robert G. Wilson v and Emeric Deutsch, Jun 25 2005
Comments