login
A047417
Numbers that are congruent to {2, 3, 4, 6} mod 8.
1
2, 3, 4, 6, 10, 11, 12, 14, 18, 19, 20, 22, 26, 27, 28, 30, 34, 35, 36, 38, 42, 43, 44, 46, 50, 51, 52, 54, 58, 59, 60, 62, 66, 67, 68, 70, 74, 75, 76, 78, 82, 83, 84, 86, 90, 91, 92, 94, 98, 99, 100, 102, 106, 107, 108, 110, 114, 115, 116, 118, 122, 123
OFFSET
1,1
FORMULA
G.f.: x*(2+x+x^2+2*x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011
From Wesley Ivan Hurt, May 25 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-5-i^(2*n)-(1-2*i)*i^(-n)-(1+2*i)*i^n)/4 with i=sqrt(-1).
a(2k) = A047398(k), a(2k-1) = A047463(k). (End)
E.g.f.: 2 + sin(x) - cos(x)/2 + (2*x - 1)*sinh(x) + (2*x - 3/2)*cosh(x). - Ilya Gutkovskiy, May 25 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (3-sqrt(2))*Pi/16 - (sqrt(2)+4)*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 25 2021
MAPLE
A047417:=n->(8*n-5-I^(2*n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4: seq(A047417(n), n=1..100); # Wesley Ivan Hurt, May 25 2016
MATHEMATICA
Flatten[#+{2, 3, 4, 6}&/@(8Range[0, 20])] (* Harvey P. Dale, Dec 20 2012 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [2, 3, 4, 6]]; // Wesley Ivan Hurt, May 25 2016
CROSSREFS
Sequence in context: A353562 A347733 A347798 * A066936 A067027 A275108
KEYWORD
nonn,easy
STATUS
approved