A047328 Numbers that are congruent to {0, 3, 5, 6} mod 7.

0, 3, 5, 6, 7, 10, 12, 13, 14, 17, 19, 20, 21, 24, 26, 27, 28, 31, 33, 34, 35, 38, 40, 41, 42, 45, 47, 48, 49, 52, 54, 55, 56, 59, 61, 62, 63, 66, 68, 69, 70, 73, 75, 76, 77, 80, 82, 83, 84, 87, 89, 90, 91, 94, 96, 97, 98, 101, 103, 104, 105, 108, 110, 111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Indices of the odd numbers in the Padovan sequence (A000931). - Francesco Daddi, Jul 31 2011

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A000931, A047280, A047382, A134719.

Programs

Magma

[ n: n in [0..111] | n mod 7 in [0,3,5,6] ]; // Bruno Berselli, Aug 01 2011

Maple

A047328:=n->(14*n-7+I^(2*n)-(1+3*I)*I^(-n)-(1-3*I)*I^n)/8: seq(A047328(n), n=1..100); # Wesley Ivan Hurt, May 31 2016

Mathematica

Table[(14n-7+I^(2n)-(1+3*I)*I^(-n)-(1-3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 31 2016 *)

PARI

a(n)=n\4*7+[0,3,5,6][n%4+1] \\ Charles R Greathouse IV, Jul 31 2011

Formula

G.f.: x^2*(3+2x+x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). a(n) = A028762(n-2), 2R. J. Mathar, Oct 18 2008

a(n) = (1/8)*(14*n-5-(2-(-1)^n)*(1+2*(-1)^floor(n/2))). - Bruno Berselli, Aug 01 2011

From Wesley Ivan Hurt, May 31 2016: (Start)

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

a(n) = (14*n-7+i^(2*n)-(1+3*i)*i^(-n)-(1-3*i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047280(k), a(2k-1) = A047382(k). (End)

E.g.f.: (4 - 3*sin(x) - cos(x) + (7*x - 4)*sinh(x) + (7*x - 3)*cosh(x))/4. - Ilya Gutkovskiy, May 31 2016