A047279 Numbers that are congruent to {0, 1, 2, 6} mod 7.
0, 1, 2, 6, 7, 8, 9, 13, 14, 15, 16, 20, 21, 22, 23, 27, 28, 29, 30, 34, 35, 36, 37, 41, 42, 43, 44, 48, 49, 50, 51, 55, 56, 57, 58, 62, 63, 64, 65, 69, 70, 71, 72, 76, 77, 78, 79, 83, 84, 85, 86, 90, 91, 92, 93, 97, 98, 99, 100, 104, 105, 106, 107, 111, 112
Offset: 1
Links
- Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Magma
[n : n in [0..100] | n mod 7 in [0, 1, 2, 6]]; // Wesley Ivan Hurt, May 21 2016
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Maple
A047279:=n->(14*n-17+3*(I^(2*n)+(1+I)*I^(-n)+(1-I)*I^n))/8: seq(A047279(n), n=1..100); # Wesley Ivan Hurt, May 21 2016
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Mathematica
LinearRecurrence[{1,0,0,1,-1},{0,1,2,6,7},80] (* Harvey P. Dale, Jun 15 2015 *)
Formula
G.f.: x^2*(1+x+4*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
From Wesley Ivan Hurt, May 21 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (14n-17+3*(i^(2n)+(1+i)*i^(-n)+(1-i)*i^n))/8 where i = sqrt(-1).
Extensions
More terms from Wesley Ivan Hurt, May 21 2016