A047490 Numbers that are congruent to {0, 1, 2, 3, 5, 7} mod 8.

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

Michael De Vlieger, Table of n, a(n) for n = 1..10001

Giulio Cerbai, Pattern-avoiding modified ascent sequences, arXiv:2401.10027 [math.CO], 2024. See p. 28.

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

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

Cf. A047450, A047549.

Sequence in context: A153088 A162535 A279814 * A357065 A039072 A055977

Adjacent sequences: A047487 A047488 A047489 * A047491 A047492 A047493

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved