login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047344 Numbers that are congruent to {0, 1, 3, 4} mod 7. 1
0, 1, 3, 4, 7, 8, 10, 11, 14, 15, 17, 18, 21, 22, 24, 25, 28, 29, 31, 32, 35, 36, 38, 39, 42, 43, 45, 46, 49, 50, 52, 53, 56, 57, 59, 60, 63, 64, 66, 67, 70, 71, 73, 74, 77, 78, 80, 81, 84, 85, 87, 88, 91, 92, 94, 95, 98, 99, 101, 102, 105, 106, 108, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=3 and b(k)=7*2^(k-2) for k>1. - Philippe Deléham, Oct 17 2011

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

From Wesley Ivan Hurt, May 23 2016: (Start)

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

a(n) = (14n-19-3*i^(2n)-(1-i)*i^(-n)-(1+i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047346(n), a(2n-1) = A047355(n). (End)

E.g.f.: (12 + sin(x) - cos(x) + (7*x - 8)*sinh(x) + (7*x - 11)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016

MAPLE

A047344:=n->(14*n-19-3*I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/8: seq(A047344(n), n=1..100); # Wesley Ivan Hurt, May 23 2016

MATHEMATICA

Table[(14n-19-3*I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 23 2016 *)

PROG

(PARI) forstep(n=0, 200, [1, 2, 1, 3], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

(MAGMA) [n : n in [0..150] | n mod 7 in [0, 1, 3, 4]]; // Wesley Ivan Hurt, May 23 2016

CROSSREFS

Cf. A030308, A047346, A047355.

Sequence in context: A046541 A324470 A219897 * A005187 A184835 A184823

Adjacent sequences:  A047341 A047342 A047343 * A047345 A047346 A047347

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 23 2016

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 07:06 EDT 2020. Contains 337267 sequences. (Running on oeis4.)