login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A047340
Numbers that are congruent to {0, 2, 3, 4} mod 7.
1
0, 2, 3, 4, 7, 9, 10, 11, 14, 16, 17, 18, 21, 23, 24, 25, 28, 30, 31, 32, 35, 37, 38, 39, 42, 44, 45, 46, 49, 51, 52, 53, 56, 58, 59, 60, 63, 65, 66, 67, 70, 72, 73, 74, 77, 79, 80, 81, 84, 86, 87, 88, 91, 93, 94, 95, 98, 100, 101, 102, 105, 107, 108, 109, 112
OFFSET
1,2
FORMULA
G.f.: x^2*(2+x+x^2+3*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011
From Wesley Ivan Hurt, May 21 2016: (Start)
a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.
a(n) = (14n-17-i^(2n)-(3-i)*i^(-n)-(3+i)*i^n)/8 where i=sqrt(-1).
a(2n) = A047348(n), a(2n-1) = A047355(n). (End)
MAPLE
A047340:=n->(14*n-17-I^(2*n)-(3-I)*I^(-n)-(3+I)*I^n)/8: seq(A047340(n), n=1..100); # Wesley Ivan Hurt, May 21 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{0, 2, 3, 4}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 0, 1, -1}, {0, 2, 3, 4, 7}, 100] (* Harvey P. Dale, Feb 16 2014 *)
CoefficientList[Series[x (2 + x + x^2 + 3 x^3)/((1 + x) (1 + x^2) (x - 1)^2), {x, 0, 200}], x] (* Vincenzo Librandi, Feb 17 2014 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [0, 2, 3, 4]]; // Vincenzo Librandi, Feb 17 2014
CROSSREFS
Sequence in context: A141489 A060253 A066276 * A270711 A096118 A050029
KEYWORD
nonn,easy
EXTENSIONS
More terms from Vincenzo Librandi, Feb 17 2014
STATUS
approved