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