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%I #37 Sep 08 2022 08:44:57
%S 0,3,5,6,7,10,12,13,14,17,19,20,21,24,26,27,28,31,33,34,35,38,40,41,
%T 42,45,47,48,49,52,54,55,56,59,61,62,63,66,68,69,70,73,75,76,77,80,82,
%U 83,84,87,89,90,91,94,96,97,98,101,103,104,105,108,110,111
%N Numbers that are congruent to {0, 3, 5, 6} mod 7.
%C Indices of the odd numbers in the Padovan sequence (A000931). - _Francesco Daddi_, Jul 31 2011
%H Bruno Berselli, <a href="/A047328/b047328.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F G.f.: x^2*(3+2x+x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). a(n) = A028762(n-2), 2<n<28. - _R. J. Mathar_, Oct 18 2008
%F a(n) = (1/8)*(14*n-5-(2-(-1)^n)*(1+2*(-1)^floor(n/2))). - _Bruno Berselli_, Aug 01 2011
%F From _Wesley Ivan Hurt_, May 31 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (14*n-7+i^(2*n)-(1+3*i)*i^(-n)-(1-3*i)*i^n)/8 where i=sqrt(-1).
%F a(2k) = A047280(k), a(2k-1) = A047382(k). (End)
%F 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
%p 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
%t Table[(14n-7+I^(2n)-(1+3*I)*I^(-n)-(1-3*I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, May 31 2016 *)
%o (PARI) a(n)=n\4*7+[0,3,5,6][n%4+1] \\ _Charles R Greathouse IV_, Jul 31 2011
%o (Magma) [ n: n in [0..111] | n mod 7 in [0,3,5,6] ]; // _Bruno Berselli_, Aug 01 2011
%Y Cf. A000931, A047280, A047382, A134719.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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