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Second row of A113435.
1

%I #16 Jul 08 2024 21:33:08

%S 1,3,11,41,154,581,2197,8317,31501,119338,452141,1713111,6490879,

%T 24593701,93184802,353074657,1337790401,5068852073,19205744921,

%U 72770053106,275723780329,1044710007771,3958378188707,14998188734897

%N Second row of A113435.

%H G. C. Greubel, <a href="/A113437/b113437.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,11,-1).

%F a(n) = A113435(3*n+1).

%F a(n) = 7*a(n-1) - 15*a(n-2) + 11*a(n-3) - a(n-4).

%F G.f.: (1-4*x+5*x^2-2*x^3)/(1-7*x+15*x^2-11*x^3+x^4).

%t CoefficientList[Series[(1 - 4*x + 5*x^2 - 2*x^3)/(1 - 7*x + 15*x^2 - 11*x^3 + x^4), {x,0,50}], x] (* _G. C. Greubel_, Mar 11 2017 *)

%t LinearRecurrence[{7,-15,11,-1},{1,3,11,41},30] (* _Harvey P. Dale_, May 09 2018 *)

%o (PARI) x='x+O('x^50); Vec((1-4*x+5*x^2-2*x^3)/(1-7*x+15*x^2-11*x^3+x^4)) \\ _G. C. Greubel_, Mar 11 2017

%Y Cf. A113435.

%K nonn,easy

%O 0,2

%A _Floor van Lamoen_, Nov 04 2005