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A047441
Numbers that are congruent to {0, 2, 5, 6} mod 8.
1
0, 2, 5, 6, 8, 10, 13, 14, 16, 18, 21, 22, 24, 26, 29, 30, 32, 34, 37, 38, 40, 42, 45, 46, 48, 50, 53, 54, 56, 58, 61, 62, 64, 66, 69, 70, 72, 74, 77, 78, 80, 82, 85, 86, 88, 90, 93, 94, 96, 98, 101, 102, 104, 106, 109, 110, 112, 114, 117, 118, 120, 122, 125
OFFSET
1,2
FORMULA
G.f.: x^2*(2+3*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011
From Wesley Ivan Hurt, May 26 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-7-i^(2*n)-i^(1-n)+i^(1+n))/4 where i=sqrt(-1).
a(2k) = A130824(k) k>0, a(2k-1) = A047615(k). (End)
E.g.f.: (4 - sin(x) + (4*x - 3)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
a(n) = (8*n-7-cos(n*Pi)-2*sin(n*Pi/2))/4. - Wesley Ivan Hurt, Oct 05 2017
Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (4-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8. - Amiram Eldar, Dec 21 2021
MAPLE
A047441:=n->(8*n-7-I^(2*n)-I^(1-n)+I^(1+n))/4: seq(A047441(n), n=1..100); # Wesley Ivan Hurt, May 26 2016
MATHEMATICA
Table[(8n-7-I^(2n)-I^(1-n)+I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 5, 6, 8}, 100] (* Harvey P. Dale, Dec 25 2023 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 5, 6]]; // Wesley Ivan Hurt, May 26 2016
CROSSREFS
Sequence in context: A121411 A224889 A363676 * A284777 A344312 A081083
KEYWORD
nonn,easy
STATUS
approved