A047297 Numbers that are congruent to {0, 3, 4, 6} mod 7.

0, 3, 4, 6, 7, 10, 11, 13, 14, 17, 18, 20, 21, 24, 25, 27, 28, 31, 32, 34, 35, 38, 39, 41, 42, 45, 46, 48, 49, 52, 53, 55, 56, 59, 60, 62, 63, 66, 67, 69, 70, 73, 74, 76, 77, 80, 81, 83, 84, 87, 88, 90, 91, 94, 95, 97, 98, 101, 102, 104, 105, 108, 109, 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*(3+x+2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 02 2016: (Start)

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

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

a(2k) = A047280(k), a(2k-1) = A047345(k). (End)

Maple

A047297:=n->(14*n-9+3*I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/8: seq(A047297(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

Mathematica

Table[(14n-9+3*I^(2n)-(1+I)*I^(-n)-(1-I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 3, 4, 6]]; // Wesley Ivan Hurt, Jun 02 2016

Crossrefs

Cf. A047280, A047345.

Sequence in context: A347752 A060832 A341292 * A183233 A191926 A065135

Adjacent sequences: A047294 A047295 A047296 * A047298 A047299 A047300

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved