A218155 Numbers congruent to 2, 3, 6, 11 mod 12.
2, 3, 6, 11, 14, 15, 18, 23, 26, 27, 30, 35, 38, 39, 42, 47, 50, 51, 54, 59, 62, 63, 66, 71, 74, 75, 78, 83, 86, 87, 90, 95, 98, 99, 102, 107, 110, 111, 114, 119, 122, 123, 126, 131, 134, 135, 138, 143, 146, 147, 150, 155, 158, 159, 162, 167, 170, 171, 174
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
Programs
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Mathematica
LinearRecurrence[{2, -2, 2, -1}, {2, 3, 6, 11}, 100] (* T. D. Noe, Nov 11 2012 *) -
PARI
for(m=2,175,if(binomial(m,4)%binomial(m,2)==0,print1(m,", "))) \\ Hugo Pfoertner, Aug 11 2020
Formula
a(n) = 2a(n-1) - 2a(n-2) + 2a(n-3) - a(n-4). - Charles R Greathouse IV, Nov 09 2012
G.f.: x^2*(x^3+4*x^2-x+2) / ((x-1)^2*(x^2+1)). - Colin Barker, Jan 07 2013
{m>1|C(m,4)==0 (mod C(m,2))}. - Gary Detlefs, Jan 11 2014
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(3)+1)*Pi/24 - log(2+sqrt(3))/(4*sqrt(3)) - log(2)/6. - Amiram Eldar, Mar 18 2022
Extensions
Edited by Andrey Zabolotskiy, Aug 11 2020