A047335 Numbers that are congruent to {0, 6} mod 7.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Links

• Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Crossrefs

Cf. A274406.

Programs

Mathematica

Select[Range[0,200],MemberQ[{0,6},Mod[#,7]]&]  (* Harvey P. Dale, Mar 16 2011 *)

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