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A047558
Numbers that are congruent to {1, 3, 6, 7} mod 8.
1
1, 3, 6, 7, 9, 11, 14, 15, 17, 19, 22, 23, 25, 27, 30, 31, 33, 35, 38, 39, 41, 43, 46, 47, 49, 51, 54, 55, 57, 59, 62, 63, 65, 67, 70, 71, 73, 75, 78, 79, 81, 83, 86, 87, 89, 91, 94, 95, 97, 99, 102, 103, 105, 107, 110, 111, 113, 115, 118, 119, 121, 123, 126
OFFSET
1,2
FORMULA
From Wesley Ivan Hurt, May 29 2016: (Start)
G.f.: x*(1+2*x+3*x^2+x^3+x^4) / ((x-1)^2*(1+x+x^2+x^3)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-3-i^(2*n)-i^(1-n)+i^(1+n))/4 where i=sqrt(-1).
a(2k) = A004767(k-1) for k>0, a(2k-1) = A047452(k). (End)
E.g.f.: (2 - sin(x) + (4*x - 1)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, May 30 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2+sqrt(2))*Pi/16 + sqrt(2)*log(2+sqrt(2))/8 - (2+sqrt(2))*log(2)/16. - Amiram Eldar, Dec 24 2021
MAPLE
A047558:=n->(8*n-3-I^(2*n)-I^(1-n)+I^(1+n))/4: seq(A047558(n), n=1..100); # Wesley Ivan Hurt, May 29 2016
MATHEMATICA
Select[Range[150], MemberQ[{1, 3, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Jul 31 2014 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 6, 7]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
Sequence in context: A026406 A289182 A188974 * A160217 A228014 A188971
KEYWORD
nonn,easy
STATUS
approved