A047324 Numbers that are congruent to {0, 2, 5, 6} mod 7.

0, 2, 5, 6, 7, 9, 12, 13, 14, 16, 19, 20, 21, 23, 26, 27, 28, 30, 33, 34, 35, 37, 40, 41, 42, 44, 47, 48, 49, 51, 54, 55, 56, 58, 61, 62, 63, 65, 68, 69, 70, 72, 75, 76, 77, 79, 82, 83, 84, 86, 89, 90, 91, 93, 96, 97, 98, 100, 103, 104, 105, 107, 110, 111

Offset

1,2

Links

Table of n, a(n) for n=1..64.

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

Formula

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

From Wesley Ivan Hurt, Jun 03 2016: (Start)

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

a(n) = (14*n - 9 - i^(2*n) + (1 - 3*i)*i^(-n) + (1 + 3*i)*i^n)/8 where i = sqrt(-1).

a(2k) = A047276(k), a(2k-1) = A047382(k). (End)

E.g.f.: (4 - 3*sin(x) + cos(x) + (7*x - 4)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016

Maple

A047324:=n->(14*n-9-I^(2*n)+(1-3*I)*I^(-n)+(1+3*I)*I^n)/8: seq(A047324(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

Mathematica

Table[(14n - 9 - I^(2n) + (1 - 3 * I) * I^(-n) + (1 + 3 * I) * I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)
Flatten[Table[7n + {0, 2, 5, 6}, {n, 0, 15}]] (* Alonso del Arte, Jun 04 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 5, 6, 7}, 80] (* Harvey P. Dale, Jan 10 2023 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 2, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016

Crossrefs

Cf. A047276, A047382.

Sequence in context: A369962 A102657 A202115 * A327184 A362265 A057894

Adjacent sequences: A047321 A047322 A047323 * A047325 A047326 A047327

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved