A047344 Numbers that are congruent to {0, 1, 3, 4} mod 7.

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

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 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 3, 4, 7}, 80] (* Harvey P. Dale, May 06 2021 *)

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