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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 (list; graph; refs; listen; history; text; internal format)
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.

FORMULA

a(n) = 7*n-a(n-1)-8 for n>1, a(1)=0. [Vincenzo Librandi, Aug 05 2010]

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: A069198 A069136 A277137 * A182623 A127020 A154662

Adjacent sequences:  A047332 A047333 A047334 * A047336 A047337 A047338

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 22 07:48 EDT 2019. Contains 328315 sequences. (Running on oeis4.)