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

1,2

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

Links

Table of n, a(n) for n=1..49.

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

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

Adjacent sequences: A047332 A047333 A047334 * A047336 A047337 A047338

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved