login
A047335
Numbers that are congruent to {0, 6} mod 7.
5
0, 6, 7, 13, 14, 20, 21, 27, 28, 34, 35, 41, 42, 48, 49, 55, 56, 62, 63, 69, 70, 76, 77, 83, 84, 90, 91, 97, 98, 104, 105, 111, 112, 118, 119, 125, 126, 132, 133, 139, 140, 146, 147, 153, 154, 160, 161, 167, 168
OFFSET
1,2
REFERENCES
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
FORMULA
From Bruno Berselli, Oct 06 2010: (Start)
G.f.: x^2*(6+x)/((1+x)*(1-x)^2).
a(n) - a(n-1) - a(n-2) + a(n-3) = 0 (n > 3).
a(n) = (14*n + 5*(-1)^n - 9)/4.
a(n) - a(n-2) = 7 (n > 2).
a(n) - a(n-1) = A010687(k) with n > 1 and k == n-1 (mod 2). (End)
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
MATHEMATICA
Select[Range[0, 200], MemberQ[{0, 6}, Mod[#, 7]]&] (* Harvey P. Dale, Mar 16 2011 *)
CROSSREFS
Cf. A274406.
Sequence in context: A069136 A348368 A277137 * A182623 A127020 A154662
KEYWORD
nonn,easy
STATUS
approved