cp's OEIS Frontend

A379211 List of positive integers that are congruent to {2, 7, 8, 13} mod 15.

%I A379211 #14 Dec 24 2024 07:29:56
%S A379211 2,7,8,13,17,22,23,28,32,37,38,43,47,52,53,58,62,67,68,73,77,82,83,88,
%T A379211 92,97,98,103,107,112,113,118,122,127,128,133,137,142,143,148,152,157,
%U A379211 158,163,167,172,173,178,182,187,188,193,197,202,203,208,212,217,218,223,227,232,233,238,242,247,248,253,257,262
%N A379211 List of positive integers that are congruent to {2, 7, 8, 13} mod 15.
%H A379211 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A379211 a(n) = 15 + a(n-4); a(n) = - a(1-n).
%F A379211 a(n) = a(n-1) + a(n-4) - a(n-5) for n > 6.
%F A379211 G.f.: x*(x^2 + 3*x + 1)*(2*x^2 - x + 2)/((1 + x)*(1 - x)^2*(1 + x^2)).
%F A379211 a(n)^2 = 15 * A379210(n) + 4.
%F A379211 For n >= 2, a(n-1) + a(n+1) = A072703(n).
%F A379211 It appears that a(n) + a(n+1) = (3/2) * A315211(n).
%F A379211 E.g.f.: (8 - 3*cos(x) + 5*(3*x - 1)*cosh(x) + 3*sin(x) + 5*(3*x - 2)*sinh(x))/4. - _Stefano Spezia_, Dec 23 2024
%F A379211 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi/(5*sqrt(3)*phi), where phi is the golden ratio (A001622). - _Amiram Eldar_, Dec 24 2024
%p A379211 a := proc(n) option remember;
%p A379211       `if`(n < 5, [0, 2, 7, 8, 13][n+1], 15 + a(n-4))
%p A379211      end:
%p A379211 seq(a(n), n = 1..70);
%t A379211 LinearRecurrence[{1, 0, 0, 1, -1}, {2, 7, 8, 13, 17}, 70] (* _Amiram Eldar_, Dec 24 2024 *)
%Y A379211 Cf. A001622, A072703, A151972, A204542, A315211, A379210.
%K A379211 nonn,easy
%O A379211 1,1
%A A379211 _Peter Bala_, Dec 18 2024