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A163346 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

%I A163346 #24 Sep 08 2022 08:45:46
%S A163346 1,7,47,309,2009,12983,83623,537621,3452881,22163527,142219007,
%T A163346 912428949,5853252329,37546657463,240841771063,1544844588981,
%U A163346 9909085155361,63559426007047,407685301497167,2614986216809589,16773100233661049,107586319349989943
%N A163346 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
%C A163346 Binomial transform of A163350. Fifth binomial transform of A163403.
%H A163346 Matthew House, <a href="/A163346/b163346.txt">Table of n, a(n) for n = 0..1000</a>
%H A163346 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F A163346 a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
%F A163346 a(n) = ((1+sqrt(2))*(5+sqrt(2))^n + (1-sqrt(2))*(5-sqrt(2))^n)/2.
%F A163346 G.f.: (1-3*x)/(1-10*x+23*x^2).
%F A163346 E.g.f.: (sqrt(2)*sinh(sqrt(2)*x) + cosh(sqrt(2)*x))*exp(5*x). - _Ilya Gutkovskiy_, Jun 30 2016
%t A163346 CoefficientList[Series[(1 - 3 x)/(1 - 10 x + 23 x^2), {x, 0, 21}], x] (* _Michael De Vlieger_, Jun 30 2016 *)
%t A163346 LinearRecurrence[{10,-23}, {1, 7}, 50] (* _G. C. Greubel_, Dec 19 2016 *)
%o A163346 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 26 2009
%o A163346 (PARI) Vec((1-3*x)/(1-10*x+23*x^2) + O(x^99)) \\ _Altug Alkan_, Jul 05 2016
%Y A163346 Cf. A163350, A163403.
%K A163346 nonn,easy
%O A163346 0,2
%A A163346 Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009
%E A163346 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 26 2009
%E A163346 New name from _G. C. Greubel_, Dec 19 2016