A047404 Numbers that are congruent to {1, 2, 3, 6} mod 8.
1, 2, 3, 6, 9, 10, 11, 14, 17, 18, 19, 22, 25, 26, 27, 30, 33, 34, 35, 38, 41, 42, 43, 46, 49, 50, 51, 54, 57, 58, 59, 62, 65, 66, 67, 70, 73, 74, 75, 78, 81, 82, 83, 86, 89, 90, 91, 94, 97, 98, 99, 102, 105, 106, 107, 110, 113, 114, 115, 118, 121, 122, 123
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
Programs
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Magma
[n : n in [0..150] | n mod 8 in [1, 2, 3, 6]]; // Wesley Ivan Hurt, May 30 2016
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Maple
A047404:=n->(4*n-4+I^(1-n)-I^(1+n))/2: seq(A047404(n), n=1..100); # Wesley Ivan Hurt, May 30 2016
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Mathematica
Table[(4n-4+I^(1-n)-I^(1+n))/2, {n, 80}] (* Wesley Ivan Hurt, May 30 2016 *) LinearRecurrence[{2,-2,2,-1},{1,2,3,6},70] (* Harvey P. Dale, Sep 15 2024 *) -
PARI
a(n)=(n-1)\4*8+[6,1,2,3][n%4+1] \\ Charles R Greathouse IV, Jun 11 2015
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Sage
[lucas_number1(n,0,1)+2*n-2 for n in range(1,56)] # Zerinvary Lajos, Jul 06 2008
Formula
a(n) = A056594(n) + 2*n-2. - Zerinvary Lajos, Jul 06 2008
G.f.: x*(1+x)*(2*x^2-x+1)/((x^2+1)*(x-1)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 30 2016: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
a(n) = (4*n-4+i^(1-n)-i^(1+n))/2 where i = sqrt(-1).
E.g.f.: 2 + sin(x) + 2*(x - 1)*exp(x). - Ilya Gutkovskiy, May 30 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/8 + log(2)/4. - Amiram Eldar, Dec 23 2021