login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047377 Numbers that are congruent to {0, 1, 4, 5} mod 7. 1

%I #29 Sep 08 2022 08:44:57

%S 0,1,4,5,7,8,11,12,14,15,18,19,21,22,25,26,28,29,32,33,35,36,39,40,42,

%T 43,46,47,49,50,53,54,56,57,60,61,63,64,67,68,70,71,74,75,77,78,81,82,

%U 84,85,88,89,91,92,95,96,98,99,102,103,105,106,109,110

%N Numbers that are congruent to {0, 1, 4, 5} mod 7.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=4 and b(k)=7*2^(k-2) for k>1. - _Philippe Deléham_, Oct 25 2011

%F G.f.: x^2*(1+3*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011

%F From _Wesley Ivan Hurt_, May 24 2016: (Start)

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

%F a(n) = (14*n-15-3*i^(2*n)+(1-i)*i^(-n)+(1+i)*i^n)/8, where i=sqrt(-1).

%F a(2k) = A047383(k), a(2k-1) = A047345(k). (End)

%F E.g.f.: (8 - sin(x) + cos(x) + (7*x - 6)*sinh(x) + (7*x - 9)*cosh(x))/4. - _Ilya Gutkovskiy_, May 25 2016

%p A047377:=n->(14*n-15-3*I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/8: seq(A047377(n), n=1..100); # _Wesley Ivan Hurt_, May 24 2016

%t Table[(14n-15-3*I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, May 24 2016 *)

%t Select[Range@ 120, MemberQ[{0, 1, 4, 5}, Mod[#, 7]] &] (* _Michael De Vlieger_, May 24 2016 *)

%t a[n_] := n + Floor[(n - 1)/2] + Floor[(n - 3)/4];

%t Table[a[n], {n, 1, 64}] (* _Peter Luschny_, Dec 23 2021 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [0, 1, 4, 5]]; // _Wesley Ivan Hurt_, May 24 2016

%Y Cf. A030308, A047345, A047383.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Wesley Ivan Hurt_, May 24 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:03 EDT 2024. Contains 371239 sequences. (Running on oeis4.)