A047371 Numbers that are congruent to {0, 2, 3, 5} mod 7.
0, 2, 3, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 24, 26, 28, 30, 31, 33, 35, 37, 38, 40, 42, 44, 45, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 86, 87, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 107, 108, 110
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
-
Magma
[n : n in [0..150] | n mod 7 in [0, 2, 3, 5]]; // Wesley Ivan Hurt, Jun 04 2016
-
Maple
seq(floor((7*n-6)/4), n=1..56); # [Gary Detlefs, Mar 06 2010]
-
Mathematica
Table[I^(-n)*((14n-15)*I^n+I-1-(1+I)*I^(2n)+I^(-n))/8, {n, 80}] (* Wesley Ivan Hurt, Jun 04 2016 *) LinearRecurrence[{1,0,0,1,-1},{0,2,3,5,7},70] (* Harvey P. Dale, Oct 24 2018 *)
Formula
a(n) = floor((7n-6)/4). [Gary Detlefs, Mar 06 2010]
G.f.: x^2*(2+x+2*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011
From Wesley Ivan Hurt, Jun 04 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = i^(-n)*((14*n-15)*i^n+i-1-(1+i)*i^(2*n)+i^(-n))/8 where i=sqrt(-1).
E.g.f.: (8 + sin(x) - cos(x) + (7*x - 8)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016