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A047322
Numbers that are congruent to {0, 1, 5, 6} mod 7.
2
0, 1, 5, 6, 7, 8, 12, 13, 14, 15, 19, 20, 21, 22, 26, 27, 28, 29, 33, 34, 35, 36, 40, 41, 42, 43, 47, 48, 49, 50, 54, 55, 56, 57, 61, 62, 63, 64, 68, 69, 70, 71, 75, 76, 77, 78, 82, 83, 84, 85, 89, 90, 91, 92, 96, 97, 98, 99, 103, 104, 105, 106, 110, 111
OFFSET
1,3
FORMULA
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=5, b(k)=7*2^(k-2) for k>1. - Philippe Deléham, Oct 19 2011
G.f.: x^2*(1+4*x+x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 03 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-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8 where I=sqrt(-1).
a(2n) = A047336(n), a(2n-1) = A047382(n). (End)
E.g.f.: (4 - 3*sin(x) + 3*cos(x) + (7*x - 4)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016
MAPLE
A047322:=n->(14*n-11-3*I^(2*n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8: seq(A047322(n), n=1..100); # Wesley Ivan Hurt, May 23 2016
MATHEMATICA
Table[(14n-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 23 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 5, 6, 7}, 60] (* Vincenzo Librandi, May 24 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 5, 6]]; // Wesley Ivan Hurt, May 23 2016
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from Wesley Ivan Hurt, May 23 2016
STATUS
approved