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A047613
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Numbers that are congruent to {1, 2, 4, 5} mod 8.
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2
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1, 2, 4, 5, 9, 10, 12, 13, 17, 18, 20, 21, 25, 26, 28, 29, 33, 34, 36, 37, 41, 42, 44, 45, 49, 50, 52, 53, 57, 58, 60, 61, 65, 66, 68, 69, 73, 74, 76, 77, 81, 82, 84, 85, 89, 90, 92, 93, 97, 98, 100, 101, 105, 106, 108, 109, 113, 114, 116, 117, 121, 122, 124
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
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From Bruno Berselli, Jul 17 2012: (Start)
G.f.: x*(1+x+2*x^2+x^3+3*x^4)/((1+x)*(1-x)^2*(1+x^2)).
a(n) = 2*n-2-((-1)^n+i^(n*(n+1)))/2, where i=sqrt(-1). (End)
From Wesley Ivan Hurt, Jun 02 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(2k) = A047617(k), a(2k-1) = A047461(k). (End)
E.g.f.: (6 + sin(x) - cos(x) + (4*x - 3)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/4 - (sqrt(2)+1)*log(2)/8. - Amiram Eldar, Dec 23 2021
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MAPLE
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A047613:=n->2*n-2-(I^(2*n)+I^(n*(n+1)))/2: seq(A047613(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016
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MATHEMATICA
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Select[Range[120], MemberQ[{1, 2, 4, 5}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 4, 5, 9}, 60] (* Bruno Berselli, Jul 17 2012 *)
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PROG
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From Bruno Berselli, Jul 17 2012: (Start)
(Magma) [n: n in [1..120] | n mod 8 in [1, 2, 4, 5]];
(Maxima) makelist(2*n-2-((-1)^n+%i^(n*(n+1)))/2, n, 1, 60);
(PARI) Vec((1+x+2*x^2+x^3+3*x^4)/((1+x)*(1-x)^2*(1+x^2))+O(x^60)) (End)
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CROSSREFS
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Cf. A047461, A047617.
Sequence in context: A284389 A342735 A342750 * A036795 A307563 A289175
Adjacent sequences: A047610 A047611 A047612 * A047614 A047615 A047616
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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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