A047338 Numbers that are congruent to {1, 2, 3, 4} mod 7.

1, 2, 3, 4, 8, 9, 10, 11, 15, 16, 17, 18, 22, 23, 24, 25, 29, 30, 31, 32, 36, 37, 38, 39, 43, 44, 45, 46, 50, 51, 52, 53, 57, 58, 59, 60, 64, 65, 66, 67, 71, 72, 73, 74, 78, 79, 80, 81, 85, 86, 87, 88, 92, 93, 94, 95, 99, 100, 101, 102, 106, 107, 108, 109

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. A047348, A047356.

Programs

Magma

[n : n in [0..150] | n mod 7 in [1, 2, 3, 4]]; // Wesley Ivan Hurt, May 23 2016

Maple

A047338:=n->(14*n-15-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8: seq(A047338(n), n=1..100); # Wesley Ivan Hurt, May 23 2016

Mathematica

Table[(14n-15-3*I^(2n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 23 2016 *)

Formula

G.f.: x*(1+x+x^2+x^3+3*x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, May 23 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14n-15-3*i^(2n)-(3-3*i)*i^(-n)-(3+3*i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047348(n), a(2n-1) = A047356(n). (End)

E.g.f.: (12 + 3*(sin(x) - cos(x)) + (7*x - 6)*sinh(x) + (7*x - 9)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016

Extensions

More terms from Wesley Ivan Hurt, May 23 2016