A047365 Numbers that are congruent to {0, 3, 4, 5} mod 7.

0, 3, 4, 5, 7, 10, 11, 12, 14, 17, 18, 19, 21, 24, 25, 26, 28, 31, 32, 33, 35, 38, 39, 40, 42, 45, 46, 47, 49, 52, 53, 54, 56, 59, 60, 61, 63, 66, 67, 68, 70, 73, 74, 75, 77, 80, 81, 82, 84, 87, 88, 89, 91, 94, 95, 96, 98, 101, 102, 103, 105, 108, 109, 110

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

a(1)=0, a(2)=3, a(3)=4, a(4)=5, a(5)=7, a(n)=a(n-1)+a(n-4)-a(n-5) for n>5. - Harvey P. Dale, May 26 2012

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

a(n) = (14*n-11+i^(2*n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047389(k), a(2k-1) = A047345(k). (End)

Maple

A047365:=n->(14*n-11+I^(2*n)-(3+I)*I^(-n)-(3-I)*I^n)/8: seq(A047365(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 3, 4, 5}, Mod[#, 7]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 4, 5, 7}, 60] (* Harvey P. Dale, May 26 2012 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 3, 4, 5]]; // Wesley Ivan Hurt, Jun 04 2016

Crossrefs

Cf. A047345, A047389.

Sequence in context: A105148 A370862 A072556 * A353448 A048342 A159560

Adjacent sequences: A047362 A047363 A047364 * A047366 A047367 A047368

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved