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 A047538 Numbers that are congruent to {0, 1, 4, 7} mod 8. 6
 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, 111, 112, 113, 116, 119, 120, 121, 124 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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] Nonnegative m such that floor(k*(m/4)^2) = k*floor((m/4)^2), where k can assume the values from 4 to 15. See also the second comment in A047513. [Bruno Berselli, Dec 03 2015] LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1). FORMULA From Paul Barry, Oct 27 2004: (Start) G.f.: x^2*(1+x)^2 / ((1+x^2)*(1-2*x+x^2)). E.g.f.: 2*x*exp(x)-sin(x). a(n) = 2*n-2-sin(Pi*(n-1)/2). a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>4. (End) a(n) = 2*n-2-(1+(-1)^n)*(-1)^((2*n-3)/4-(-1)^n/4)/2. - Wesley Ivan Hurt, Sep 22 2015 a(n) = (-4+(-i)^n+i^n+4*n)/2, where i = sqrt(-1). - Colin Barker, Oct 18 2015 MAPLE A047538:=n->2*n-2-sin(Pi*(n-1)/2): seq(A047538(n), n=1..80); # Wesley Ivan Hurt, Sep 22 2015 MATHEMATICA Table[2n-2-Sin[Pi*(n-1)/2], {n, 80}] (* Wesley Ivan Hurt, Sep 22 2015 *) Select[Range[0, 150], MemberQ[{0, 1, 4, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, Sep 23 2015 *) LinearRecurrence[{2, -2, 2, -1}, {0, 1, 4, 7}, 100] (* Harvey P. Dale, Aug 12 2016 *) PROG (Sage) [lucas_number1(n, 0, 1)+2*n-4 for n in (2..57)] # Zerinvary Lajos, Jul 06 2008 (MAGMA) [2*n-2-(1+(-1)^n)*(-1)^((2*n-3) div 4-(-1)^n div 4) / 2 : n in [1..80]]; // Wesley Ivan Hurt, Sep 22 2015 (MAGMA) [n: n in [0..150] | n mod 8 in {0, 1, 4, 7}]; // Vincenzo Librandi, Sep 23 2015 (PARI) a(n) = (-4+(-I)^n+I^n+4*n)/2 \\ Colin Barker, Oct 18 2015 (PARI) concat(0, Vec(x^2*(1+x)^2/((1+x^2)*(1-2*x+x^2)) + O(x^100))) \\ Colin Barker, Oct 18 2015 CROSSREFS Cf. A047404, A047431, A047546, A047557, A047578, A047620, A056594. Cf. A046055, A074231. Sequence in context: A020670 A253472 A255060 * A074231 A310938 A289631 Adjacent sequences:  A047535 A047536 A047537 * A047539 A047540 A047541 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Wesley Ivan Hurt, Sep 22 2015 G.f. adapted to offset by Colin Barker, Oct 18 2015 STATUS approved

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Last modified November 23 17:10 EST 2020. Contains 338595 sequences. (Running on oeis4.)