A047503 - OEIS

A047503

Numbers that are congruent to {0, 2, 3, 4, 5, 7} mod 8.

0, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 23, 24, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 39, 40, 42, 43, 44, 45, 47, 48, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 63, 64, 66, 67, 68, 69, 71, 72, 74, 75, 76, 77, 79, 80, 82, 83, 84, 85, 87

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..66.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

FORMULA

G.f.: x^2*(2+x+x^2+x^3+2*x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015

From Wesley Ivan Hurt, Jun 16 2016: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = (24*n-21+3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)-6*sin((1-2*n)*Pi/6))/18.

a(6k) = 8k-1, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-8. (End)

Sum_{n>=2} (-1)^n/a(n) = log(2)/8 - sqrt(2)*Pi/16 - sqrt(2)*log(99-70*sqrt(2))/16. - Amiram Eldar, Dec 27 2021

MAPLE

A047503:=n->(24*n-21+3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)-6*sin((1-2*n)*Pi/6))/18: seq(A047503(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 2, 3, 4, 5, 7, 8}, 100] (* Harvey P. Dale, Dec 25 2023 *)

PROG

(Magma) [n : n in [0..100] | n mod 8 in [0, 2, 3, 4, 5, 7]]; // Wesley Ivan Hurt, Jun 16 2016

CROSSREFS

Cf. A047424, A047587.

Sequence in context: A051705 A039082 A340608 * A228803 A037014 A261131

Adjacent sequences: A047500 A047501 A047502 * A047504 A047505 A047506

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved