A047335 - OEIS

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

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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