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A047575
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Numbers that are congruent to {0, 5, 6, 7} mod 8.
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1
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0, 5, 6, 7, 8, 13, 14, 15, 16, 21, 22, 23, 24, 29, 30, 31, 32, 37, 38, 39, 40, 45, 46, 47, 48, 53, 54, 55, 56, 61, 62, 63, 64, 69, 70, 71, 72, 77, 78, 79, 80, 85, 86, 87, 88, 93, 94, 95, 96, 101, 102, 103, 104, 109, 110, 111, 112, 117, 118, 119, 120, 125
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..62.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
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From Wesley Ivan Hurt, May 29 2016: (Start)
G.f.: x^2*(5+x+x^2+x^3) / ((x-1)^2*(1+x+x^2+x^3)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (4*n-1+i^(2*n)-(1+i)*i^(-n)-(1-i)*i^n)/2 where i=sqrt(-1).
a(2k) = A047550(k), a(2k-1) = A047451(k). (End)
E.g.f.: 1 - sin(x) - cos(x) - sinh(x) + 2*x*exp(x). - Ilya Gutkovskiy, May 30 2016
Sum_{n>=2} (-1)^n/a(n) = 5*log(2)/8 - (2*sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 23 2021
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MAPLE
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A047575:=n->(4*n-1+I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/2: seq(A047575(n), n=1..100); # Wesley Ivan Hurt, May 29 2016
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MATHEMATICA
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Select[Range[0, 120], MemberQ[{0, 5, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Jun 30 2011 *)
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PROG
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(MAGMA) [n : n in [0..150] | n mod 8 in [0, 5, 6, 7]]; // Wesley Ivan Hurt, May 29 2016
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CROSSREFS
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Cf. A047451, A047550.
Sequence in context: A080703 A284682 A171405 * A014097 A219331 A229862
Adjacent sequences: A047572 A047573 A047574 * A047576 A047577 A047578
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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