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A047490
Numbers that are congruent to {0, 1, 2, 3, 5, 7} mod 8.
2
0, 1, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 82, 83, 85, 87, 88
OFFSET
1,3
LINKS
Giulio Cerbai, Pattern-avoiding modified ascent sequences, arXiv:2401.10027 [math.CO], 2024. See p. 28.
FORMULA
G.f.: x^2*(x^4+x^3+x^2+1)/((x-1)^2*(x^2-x+1)*(x^2+x+1)). - Colin Barker, Jun 22 2012
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
a(n) = (24*n-30+6*sqrt(3)*cos((1-2n)*Pi/6)+2*sqrt(3)*cos((1+4n)*Pi/6))/18.
a(6k) = 8k-1, a(6k-1) = 8k-3, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = (2*sqrt(2)-3)*Pi/16 + (5-sqrt(2))*log(2)/8 + sqrt(2)*log(sqrt(2)+2)/4. - Amiram Eldar, Dec 26 2021
MAPLE
A047490:=n->(24*n-30+6*sqrt(3)*cos((1-2*n)*Pi/6)+2*sqrt(3)*cos((1+4*n)*Pi/6))/18: seq(A047490(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 5, 7]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
Sequence in context: A153088 A162535 A279814 * A357065 A039072 A055977
KEYWORD
nonn,easy
STATUS
approved