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A047508
Numbers that are congruent to {1, 4, 6, 7} mod 8.
1
1, 4, 6, 7, 9, 12, 14, 15, 17, 20, 22, 23, 25, 28, 30, 31, 33, 36, 38, 39, 41, 44, 46, 47, 49, 52, 54, 55, 57, 60, 62, 63, 65, 68, 70, 71, 73, 76, 78, 79, 81, 84, 86, 87, 89, 92, 94, 95, 97, 100, 102, 103, 105, 108, 110, 111, 113, 116, 118, 119, 121, 124
OFFSET
1,2
FORMULA
From Wesley Ivan Hurt, May 27 2016: (Start)
G.f.: x*(1+2*x+x^3)/( (x-1)^2*(1+x^2) ).
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
a(n) = (1+i)*(4*n-4*n*i+i-1-i^(-n)+i^(1+n))/4 where i=sqrt(-1).
a(2k) = A047535(k), a(2k-1) = A047452(k). (End)
E.g.f.: (2 - sin(x) - cos(x) + (4*x - 1)*exp(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 + log(2)/8. - Amiram Eldar, Dec 24 2021
MAPLE
A047508:=n->(1+I)*(4*n-4*n*I+I-1-I^(-n)+I^(1+n))/4: seq(A047508(n), n=1..100); # Wesley Ivan Hurt, May 27 2016
MATHEMATICA
Table[(1+I)*(4n-4*n*I+I-1-I^(-n)+I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016
CROSSREFS
Sequence in context: A085817 A177688 A190250 * A089960 A067888 A189142
KEYWORD
nonn,easy
STATUS
approved