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 A079496 a(0) = a(1) = 1; thereafter a(2*n+1) = 2*a(2*n) - a(2*n-1), a(2*n) = 4*a(2*n-1) - a(2*n-2). 12
 1, 1, 3, 5, 17, 29, 99, 169, 577, 985, 3363, 5741, 19601, 33461, 114243, 195025, 665857, 1136689, 3880899, 6625109, 22619537, 38613965, 131836323, 225058681, 768398401, 1311738121, 4478554083, 7645370045, 26102926097, 44560482149 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(1)=1, a(n) is the smallest integer > a(n-1) such that sqrt(2)*a(n) is closer and > to an integer than sqrt(2)*a(n-1) (i.e., a(n) is the smallest integer > a(n-1) such that frac(sqrt(2)*a(n))= 3 where H(n, a, b) = hypergeom([a - n/2, b - n/2], [1 - n], -1). - Peter Luschny, Sep 03 2019 EXAMPLE 1 + x + 3*x^2 + 5*x^3 + 17*x^4 + 29*x^5 + 99*x^6 + 169*x^7 + 577*x^8 + ... MAPLE H := (n, a, b) -> hypergeom([a - n/2, b - n/2], [1 - n], -1): a := n -> `if`(n < 3, [1, 1, 3][n+1], 2^(n - 1)*H(n, irem(n, 2), 1/2)): seq(simplify(a(n)), n=0..26); # Peter Luschny, Sep 03 2019 MATHEMATICA a[1] = 1; a[2] = 3; a[3] = 5; a[n_] := a[n] = (a[n-1]*a[n-2] + 2) / a[n-3]; Table[a[n], {n, 1, 29}] (* Jean-François Alcover, Jul 17 2013, after Paul D. Hanna *) PROG (PARI) {a(n) = n = abs(n); 2^((4-n)\2) * real( (10 + 7 * quadgen(8)) / 2 * (2 + quadgen(8))^(n-3) ) } /* Michael Somos, Sep 03 2013 */ (PARI) {a(n) = polcoeff( (1 + x - 3*x^2 - x^3) / (1 - 6*x^2 + x^4) + x * O(x^abs(n)), abs(n))} /* Michael Somos, Sep 03 2013 */ (Magma) [1, 1] cat [Floor((Sqrt(2)*Sqrt(2+(3-2*Sqrt(2))^n+(3+2*Sqrt(2))^(1+n)))/(2+Sqrt(2)-(-1)^n*(-2+Sqrt(2)))): n in [1..40]]; // Vincenzo Librandi, Jun 07 2015 CROSSREFS Cf. A010914, A058580, A133080. Sequence in context: A113169 A350856 A174913 * A230639 A038898 A333353 Adjacent sequences: A079493 A079494 A079495 * A079497 A079498 A079499 KEYWORD nonn,easy AUTHOR Benoit Cloitre, Jan 20 2003 EXTENSIONS a(0)=1 added by Michael Somos, Sep 03 2013 STATUS approved

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)