# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a115113 Showing 1-1 of 1 %I A115113 #24 Sep 08 2022 08:45:23 %S A115113 2,6,10,54,202,822,3274,13110,52426,209718,838858,3355446,13421770, %T A115113 53687094,214748362,858993462,3435973834,13743895350,54975581386, %U A115113 219902325558,879609302218,3518437208886,14073748835530,56294995342134,225179981368522,900719925474102 %N A115113 a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = 2, a(1) = 6, a(2) = 10. %H A115113 G. C. Greubel, Table of n, a(n) for n = 0..1000 %H A115113 Index entries for linear recurrences with constant coefficients, signature (3,4). %F A115113 From _Colin Barker_, Nov 13 2012: (Start) %F A115113 a(n) = (-2*(7*(-1)^n - 2^(1 + 2*n)))/5 for n > 0. %F A115113 a(n) = 3*a(n-1) + 4*a(n-2) for n > 2. %F A115113 G.f.: 2*(8*x^2 - 1)/((x + 1)*(4*x - 1)). (End) %F A115113 E.g.f.: (20 - 14*exp(-x) + 4*exp(4*x))/5. - _Franck Maminirina Ramaharo_, Nov 23 2018 %t A115113 Join[{2}, LinearRecurrence[{3, 4}, {6, 10}, 50]] %o A115113 (Maxima) (a[0] : 2, a[1] : 6, a[2] : 10, a[n] := 3*a[n-1] + 4*a[n-2], makelist(a[n], n, 0, 50)); /* _Franck Maminirina Ramaharo_, Nov 23 2018 */ %o A115113 (PARI) x='x+O('x^50); Vec(2*(8*x^2-1)/((x+1)*(4*x-1))) \\ _G. C. Greubel_, Nov 23 2018 %o A115113 (Magma) I:=[6,10]; [2] cat [n le 2 select I[n] else 3*Self(n-1) + 4*Self(n-2): n in [1..49]]; // _G. C. Greubel_, Nov 23 2018 %o A115113 (Sage) s=(2*(8*x^2-1)/((x+1)*(4*x-1))).series(x,50); s.coefficients(x, sparse=False) # _G. C. Greubel_, Nov 23 2018 %Y A115113 Cf. A115164, A115335. %K A115113 nonn,easy %O A115113 0,1 %A A115113 _Roger L. Bagula_, Mar 06 2006 %E A115113 Edited, and new name from _Franck Maminirina Ramaharo_, Nov 23 2018, after _Colin Barker_'s formula # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE