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 A137255 a(n) = 2a(n-1) + 4a(n-2) - 6a(n-3) - 3a(n-4). 1
 1, 2, 4, 8, 17, 36, 80, 178, 409, 942, 2212, 5204, 12377, 29472, 70592, 169198, 406801, 978426, 2357092, 5679488, 13696385, 33032892, 79703120, 192321034, 464168041, 1120302822, 2704242244, 6527724428, 15758096777, 38040729336, 91834772480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Index entries for linear recurrences with constant coefficients, signature (2,4,-6,-3). FORMULA a(n) = (3/8)*3^(n/2)*(1 + (-1)^n) + (5/24)*3^((n+1)/2)*(1 - (-1)^n) + (1/8)*(1+sqrt(2))^(n+1) + (1/8)*(1-sqrt(2))^(n+1). - Emeric Deutsch, Mar 31 2008 G.f.: (1 - 4*x^2 - 2*x^3)/(1 - 2*x - 4*x^2 + 6*x^3 + 3*x^4). - Harvey P. Dale, May 03 2018 MAPLE a:=proc(n) options operator, arrow: expand((3/8)*3^((1/2)*n)*(1+(-1)^n)+(5/24)*3^((1/2)*n+1/2)*(1-(-1)^n)+(1/8)*(1+sqrt(2))^(n+1)+(1/8)*(1-sqrt(2))^(n+1)) end proc: seq(a(n), n=0..30); # Emeric Deutsch, Mar 31 2008 MATHEMATICA LinearRecurrence[{2, 4, -6, -3}, {1, 2, 4, 8}, 40] (* or *) CoefficientList[ Series[ (1-4 x^2-2 x^3)/(1-2 x-4 x^2+6 x^3+3 x^4), {x, 0, 40}], x] (* Harvey P. Dale, May 03 2018 *) CROSSREFS Sequence in context: A002955 A202844 A093951 * A247298 A325928 A076892 Adjacent sequences:  A137252 A137253 A137254 * A137256 A137257 A137258 KEYWORD nonn AUTHOR Paul Curtz, Mar 11 2008 EXTENSIONS More terms from Emeric Deutsch, Mar 31 2008 STATUS approved

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Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)