A047377 Numbers that are congruent to {0, 1, 4, 5} mod 7.

0, 1, 4, 5, 7, 8, 11, 12, 14, 15, 18, 19, 21, 22, 25, 26, 28, 29, 32, 33, 35, 36, 39, 40, 42, 43, 46, 47, 49, 50, 53, 54, 56, 57, 60, 61, 63, 64, 67, 68, 70, 71, 74, 75, 77, 78, 81, 82, 84, 85, 88, 89, 91, 92, 95, 96, 98, 99, 102, 103, 105, 106, 109, 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. A030308, A047345, A047383.

Programs

Magma

[n : n in [0..150] | n mod 7 in [0, 1, 4, 5]]; // Wesley Ivan Hurt, May 24 2016

Maple

A047377:=n->(14*n-15-3*I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/8: seq(A047377(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

Mathematica

Table[(14n-15-3*I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)
Select[Range@ 120, MemberQ[{0, 1, 4, 5}, Mod[#, 7]] &] (* Michael De Vlieger, May 24 2016 *)
a[n_] :=  n + Floor[(n - 1)/2] +  Floor[(n - 3)/4];
Table[a[n], {n, 1, 64}] (* Peter Luschny, Dec 23 2021 *)

Formula

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=4 and b(k)=7*2^(k-2) for k>1. - Philippe Deléham, Oct 25 2011

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

From Wesley Ivan Hurt, May 24 2016: (Start)

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

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

a(2k) = A047383(k), a(2k-1) = A047345(k). (End)

E.g.f.: (8 - sin(x) + cos(x) + (7*x - 6)*sinh(x) + (7*x - 9)*cosh(x))/4. - Ilya Gutkovskiy, May 25 2016

Extensions

More terms from Wesley Ivan Hurt, May 24 2016