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A047445
Numbers that are congruent to {1, 3, 5, 6} mod 8.
1
1, 3, 5, 6, 9, 11, 13, 14, 17, 19, 21, 22, 25, 27, 29, 30, 33, 35, 37, 38, 41, 43, 45, 46, 49, 51, 53, 54, 57, 59, 61, 62, 65, 67, 69, 70, 73, 75, 77, 78, 81, 83, 85, 86, 89, 91, 93, 94, 97, 99, 101, 102, 105, 107, 109, 110, 113, 115, 117, 118, 121, 123, 125
OFFSET
1,2
FORMULA
G.f.: x*(1+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) = (8*n-5-i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).
a(2k) = A047398(k), a(2k-1) = A016813(k-1) for k>0. (End)
E.g.f.: (4 - cos(x) + (4*x - 2)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (4-sqrt(2))*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 24 2021
MAPLE
A047445:=n->(8*n-5-I^(2*n)-I^(-n)-I^n)/4: seq(A047445(n), n=1..100); # Wesley Ivan Hurt, May 26 2016
MATHEMATICA
Table[(8n-5-I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 5, 6]]; // Wesley Ivan Hurt, May 26 2016
CROSSREFS
Sequence in context: A367499 A324701 A047271 * A341349 A248638 A248881
KEYWORD
nonn,easy
STATUS
approved