A047372 Numbers that are congruent to {1, 2, 3, 5} mod 7.

1, 2, 3, 5, 8, 9, 10, 12, 15, 16, 17, 19, 22, 23, 24, 26, 29, 30, 31, 33, 36, 37, 38, 40, 43, 44, 45, 47, 50, 51, 52, 54, 57, 58, 59, 61, 64, 65, 66, 68, 71, 72, 73, 75, 78, 79, 80, 82, 85, 86, 87, 89, 92, 93, 94, 96, 99, 100, 101, 103, 106, 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. A047356, A047385.

Programs

Magma

[n : n in [0..150] | n mod 7 in [1, 2, 3, 5]]; // Wesley Ivan Hurt, Jun 04 2016

Maple

A047372:=n->(14*n+(3*I-1)*(-I)^n-(3*I+1)*I^n-(-1)^n-13)/8: seq(A047372(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

Flatten[7Range[0,12]+n/.n->{1,2,3,5}] (* Harvey P. Dale, Dec 13 2010 *)

Formula

From Bruno Berselli, Dec 01 2010: (Start)

G.f.: x*(1+x+x^2+2*x^3+2*x^4) / ((1-x)^2*(1+x+x^2+x^3)).

a(n) = (14*n+(3*i-1)*(-i)^n-(3*i+1)*i^n-(-1)^n-13)/8, i=sqrt(-1). (End)

From Wesley Ivan Hurt, Jun 04 2016: (Start)

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

a(2k) = A047385(k), a(2k-1) = A047356(k). (End)

E.g.f.: (8 + 3*sin(x) - cos(x) + (7*x - 6)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016