|
%I #36 Jul 02 2023 14:22:34
%S 0,6,7,13,14,20,21,27,28,34,35,41,42,48,49,55,56,62,63,69,70,76,77,83,
%T 84,90,91,97,98,104,105,111,112,118,119,125,126,132,133,139,140,146,
%U 147,153,154,160,161,167,168
%N Numbers that are congruent to {0, 6} mod 7.
%D Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).
%F From _Bruno Berselli_, Oct 06 2010: (Start)
%F G.f.: x^2*(6+x)/((1+x)*(1-x)^2).
%F a(n) - a(n-1) - a(n-2) + a(n-3) = 0 (n > 3).
%F a(n) = (14*n + 5*(-1)^n - 9)/4.
%F a(n) - a(n-2) = 7 (n > 2).
%F a(n) - a(n-1) = A010687(k) with n > 1 and k == n-1 (mod 2). (End)
%F a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=6 and b(k) = 7*2^(k-1) = A005009(k-1) for k > 0. - _Philippe Deléham_, Oct 18 2011
%t Select[Range[0,200],MemberQ[{0,6},Mod[#,7]]&] (* _Harvey P. Dale_, Mar 16 2011 *)
%Y Cf. A274406.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
|
