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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A047355, A047385.

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).

a(2k) = A047385(k), a(2k-1) = A047355(k). (End)

E.g.f.: (8 + sin(x) - cos(x) + (7*x - 8)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016