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A047447
Numbers that are congruent to {2, 3, 5, 6} mod 8.
3
2, 3, 5, 6, 10, 11, 13, 14, 18, 19, 21, 22, 26, 27, 29, 30, 34, 35, 37, 38, 42, 43, 45, 46, 50, 51, 53, 54, 58, 59, 61, 62, 66, 67, 69, 70, 74, 75, 77, 78, 82, 83, 85, 86, 90, 91, 93, 94, 98, 99, 101, 102, 106, 107, 109, 110, 114, 115, 117, 118, 122, 123
OFFSET
1,1
FORMULA
G.f.: x*(2+x+2*x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011
From Wesley Ivan Hurt, May 26 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (1+i)*(4*n-4*n*i+2*i-2-(1-i)*i^(2*n)+i^(1-n)-i^n)/4 where i=sqrt(-1).
a(2k) = A047398(k), a(2k-1) = A047617(k). (End)
E.g.f.: (4 + sin(x) - cos(x) + (4*x - 1)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2-sqrt(2))*Pi/8. - Amiram Eldar, Dec 25 2021
MAPLE
A047447:=n->(1+I)*(4*n-4*n*I+2*I-2-(1-I)*I^(2*n)+I^(1-n)-I^n)/4: seq(A047447(n), n=1..100); # Wesley Ivan Hurt, May 26 2016
MATHEMATICA
Table[(1+I)*(4n-4*n*I+2*I-2-(1-I)*I^(2n)+I^(1-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [2, 3, 5, 6]]; // Wesley Ivan Hurt, May 26 2016
CROSSREFS
Sequence in context: A303431 A317709 A034044 * A094739 A302494 A302534
KEYWORD
nonn,easy
STATUS
approved