The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A146963 a(n) = ((3 + sqrt(7))^n + (3 - sqrt(7))^n)/2. 4
 1, 3, 16, 90, 508, 2868, 16192, 91416, 516112, 2913840, 16450816, 92877216, 524361664, 2960415552, 16713769984, 94361788800, 532743192832, 3007735579392, 16980927090688, 95870091385344, 541258694130688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A108851. Inverse binomial transform of A146964. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..158 FORMULA From Philippe Deléham and Klaus Brockhaus, Nov 05 2008: (Start) a(n) = 6*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=3. G.f.: (1-3*x)/(1-6*x+2*x^2). (End) a(n) = (Sum_{k=0..n} A098158(n,k)*3^(2*k)*7^(n-k))/3^n. - Philippe Deléham, Nov 06 2008 E.g.f.: exp(3*x)*cosh(sqrt(7)*x). - G. C. Greubel, Jan 08 2020 MAPLE seq(coeff(series((1-3*x)/(1-6*x+2*x^2), x, n+1), x, n), n = 0..25); # G. C. Greubel, Jan 08 2020 MATHEMATICA Transpose[NestList[Join[{Last[#], 6Last[#]-2First[#]}]&, {1, 3}, 25]] [[1]]  (* or *) CoefficientList[Series[(1-3x)/(1-6x+2x^2), {x, 0, 25}], x]  (* Harvey P. Dale, Apr 11 2011 *) LinearRecurrence[{6, -2}, {1, 3}, 25] (* G. C. Greubel, Jan 08 2020 *) PROG (MAGMA) Z:= PolynomialRing(Integers()); N:=NumberField(x^2-7); S:=[ ((3+r7)^n+(3-r7)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008 (PARI) my(x='x+O('x^25)); Vec((1-3*x)/(1-6*x+2*x^2)) \\ G. C. Greubel, Jan 08 2020 (Sage) def A146963_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( (1-3*x)/(1-6*x+2*x^2) ).list() A146963_list(25) # G. C. Greubel, Jan 08 2020 (GAP) a:=[1, 3];; for n in [3..25] do a[n]:=6*a[n-1]-2*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020 CROSSREFS Cf. A098158, A108851, A146964. Sequence in context: A151329 A026111 A026330 * A074562 A130744 A009124 Adjacent sequences:  A146960 A146961 A146962 * A146964 A146965 A146966 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008 EXTENSIONS Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008 Edited by Klaus Brockhaus, Jul 16 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 13 15:23 EDT 2021. Contains 342936 sequences. (Running on oeis4.)