# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a093132 Showing 1-1 of 1 %I A093132 #17 Sep 08 2022 08:45:13 %S A093132 1,8,60,440,3200,23200,168000,1216000,8800000,63680000,460800000, %T A093132 3334400000,24128000000,174592000000,1263360000000,9141760000000, %U A093132 66150400000000,478668800000000,3463680000000000,25063424000000000 %N A093132 Third binomial transform of Fibonacci(3n+2). %H A093132 G. C. Greubel, Table of n, a(n) for n = 0..1000 %H A093132 Index entries for linear recurrences with constant coefficients, signature (10,-20). %F A093132 G.f.: (1-2*x)/(1-10*x+20*x^2). %F A093132 a(n) = ( (5 + 3*sqrt(5))*(5 + sqrt(5))^n + (5 - 3*sqrt(5))*(5 - sqrt(5))^n)/10. %F A093132 a(n) = 2^n*A039717(n). %F A093132 a(2*n) = 4^n*5^n*Fibonacci(2*n+2), a(2*n+1) = 2^(2*n+1)*5^n*Lucas(2*n+3). - _G. C. Greubel_, Dec 27 2019 %p A093132 seq(coeff(series((1-2*x)/(1-10*x+20*x^2), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Dec 27 2019 %t A093132 Table[If[EvenQ[n], 2^n*5^(n/2)*Fibonacci[n+2], 2^n*5^((n-1)/2)*LucasL[n+2]], {n, 0, 30}] (* _G. C. Greubel_, Dec 27 2019 *) %o A093132 (PARI) my(x='x+O('x^30)); Vec((1-2*x)/(1-10*x+20*x^2)) \\ _G. C. Greubel_, Dec 27 2019 %o A093132 (Magma) I:=[1,8]; [n le 2 select I[n] else 10*(Self(n-1) - 2*Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Dec 27 2019 %o A093132 (Sage) %o A093132 def A093132_list(prec): %o A093132 P. = PowerSeriesRing(ZZ, prec) %o A093132 return P( (1-2*x)/(1-10*x+20*x^2) ).list() %o A093132 A093132_list(30) # _G. C. Greubel_, Dec 27 2019 %o A093132 (GAP) a:=[1,8];; for n in [2..30] do a[n]:=10*(a[n-1]-2*a[n-2]); od; a; # _G. C. Greubel_, Dec 27 2019 %Y A093132 Cf. A000032, A000045, A039717. %K A093132 easy,nonn %O A093132 0,2 %A A093132 _Paul Barry_, Mar 23 2004 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE