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A047538
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Numbers that are congruent to {0, 1, 4, 7} mod 8.
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3
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0, 1, 4, 7, 8, 9, 12, 15, 16, 17, 20, 23, 24, 25, 28, 31, 32, 33, 36, 39, 40, 41, 44, 47, 48, 49, 52, 55, 56, 57, 60, 63, 64, 65, 68, 71, 72, 73, 76, 79, 80, 81, 84, 87, 88, 89, 92, 95, 96, 97, 100, 103, 104, 105, 108
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OFFSET
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1,3
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COMMENTS
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Related to a Chebyshev transform of A046055. See A074231. - Paul Barry, Oct 27 2004
Starting (1, 4, 7,...) = partial sums of (1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1,...). - Gary W. Adamson, Jun 19 2008
The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4 etc. - Bruno Berselli, Nov 28 2012
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LINKS
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Table of n, a(n) for n=1..55.
Index to sequences with linear recurrences with constant coefficients, signature (2,-2,2,-1)
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FORMULA
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Contribution from Paul Barry, Oct 27 2004: (Start)
G.f.: x*(1+x)^2/((1+x^2)*(1-2*x+x^2)).
E.g.f.: 2*x*exp(x)-sin(x).
a(n) = 2*n-sin(pi*n/2).
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4). (End)
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PROG
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sage: [lucas_number1(n, 0, 1)+2*n-4 for n in xrange(2, 57)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 06 2008
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CROSSREFS
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Cf. A047404, A047431, A047546, A047557, A047578, A047620, A056594.
Sequence in context: A060257 A161986 A020670 * A074231 A076680 A001074
Adjacent sequences: A047535 A047536 A047537 * A047539 A047540 A047541
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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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