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A047344
Numbers that are congruent to {0, 1, 3, 4} mod 7.
1
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
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
KEYWORD
nonn,easy
EXTENSIONS
More terms from Wesley Ivan Hurt, May 23 2016
STATUS
approved