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A047324 Numbers that are congruent to {0, 2, 5, 6} mod 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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: A153384 A102657 A202115 * A327184 A057894 A057694

Adjacent sequences:  A047321 A047322 A047323 * A047325 A047326 A047327

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 18 01:39 EDT 2021. Contains 347504 sequences. (Running on oeis4.)