A047331 Numbers that are congruent to {2, 3, 5, 6} mod 7.

2, 3, 5, 6, 9, 10, 12, 13, 16, 17, 19, 20, 23, 24, 26, 27, 30, 31, 33, 34, 37, 38, 40, 41, 44, 45, 47, 48, 51, 52, 54, 55, 58, 59, 61, 62, 65, 66, 68, 69, 72, 73, 75, 76, 79, 80, 82, 83, 86, 87, 89, 90, 93, 94, 96, 97, 100, 101, 103, 104, 107, 108, 110, 111

Offset

1,1

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+x+2*x^2+x^3+x^4) / ( (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-3-3*i^(2*n)-(1-i)*i^(-n)-(1+i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047280(k), a(2k-1) = A047385(k). (End)

Maple

A047331:=n->(14*n-3-3*I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/8: seq(A047331(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

Mathematica

Table[(14n-3-3*I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [2, 3, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016

Crossrefs

Cf. A047280, A047385.

Sequence in context: A024620 A232527 A188375 * A288480 A344633 A029451

Adjacent sequences: A047328 A047329 A047330 * A047332 A047333 A047334

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved