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 A168055 Expansion of 2 - x - sqrt(1-2x-3x^2). 4
 1, 0, 2, 2, 4, 8, 18, 42, 102, 254, 646, 1670, 4376, 11596, 31022, 83670, 227268, 621144, 1706934, 4713558, 13072764, 36398568, 101704038, 285095118, 801526446, 2259520830, 6385455594, 18086805002, 51339636952, 146015545604 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Hankel transform is A168054. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n+2) = 2*A001006(n). a(n) = 0^n + 2*Sum_{k=0..floor((n-2)/2)} C(n-2,2k)*A000108(k). 0 = a(n) * (9*a(n+1) + 15*a(n+2) - 12*a(n+3)) + a(n+1) * (-3*a(n+1) + 10*a(n+2) - 5*a(n+3)) + a(n+2) * (a(n+2) + a(n+3)) if n>0. - Michael Somos, Jan 25 2014 Conjecture: n*a(n) +(-2*n+3)*a(n-1) +3*(-n+3)*a(n-2)=0. - R. J. Mathar, Nov 19 2014 EXAMPLE G.f. = 1 + 2*x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 18*x^6 + 42*x^7 + 102*x^8 + 254*x^9 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ 2 - x - Sqrt[1 - 2 x - 3 x^2], {x, 0, n}] (* Michael Somos, Jan 25 2014 *) PROG (PARI) {a(n) = polcoeff( 2 - x - sqrt(1 - 2*x - 3*x^2 + x * O(x^n)), n)} /* Michael Somos, Jan 25 2014 */ CROSSREFS Cf. A168049. Cf. A126068, A007971. [R. J. Mathar, Nov 18 2009] Sequence in context: A007971 A126068 A167022 * A005702 A095335 A283117 Adjacent sequences:  A168052 A168053 A168054 * A168056 A168057 A168058 KEYWORD easy,nonn AUTHOR Paul Barry, Nov 17 2009 EXTENSIONS Name corrected by Michael Somos, Mar 23 2012 STATUS approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)