login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Second column of Lucas bisection triangle (even part).
4

%I #17 Aug 28 2021 18:31:59

%S 1,17,80,303,1039,3364,10493,31885,95032,279051,809771,2327372,

%T 6636025,18794633,52925984,148303719,413768263,1150029940,3185625077,

%U 8797726981,24230897416,66574108227

%N Second column of Lucas bisection triangle (even part).

%C Numerator of g.f. is row polynomial Sum_{m=0..3} A061186(2, m)*x^m.

%H G. C. Greubel, <a href="/A060934/b060934.txt">Table of n, a(n) for n = 0..1000</a>

%H É. Czabarka, R. Flórez, and L. Junes, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Florez/florez12.html">A Discrete Convolution on the Generalized Hosoya Triangle</a>, Journal of Integer Sequences, 18 (2015), #15.1.6.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).

%F a(n) = A060923(n+1, 1).

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

%F a(n) = 2*n*Lucas(2*n+2) + Fibonacci(2*n+2). - _G. C. Greubel_, Apr 09 2021

%t LinearRecurrence[{6,-11,6,-1}, {1,17,80,303}, 31] (* _G. C. Greubel_, Apr 09 2021 *)

%t CoefficientList[Series[(1+11x-11x^2+4x^3)/(1-3x+x^2)^2,{x,0,30}],x] (* _Harvey P. Dale_, Aug 28 2021 *)

%o (Magma) [2*n*Lucas(2*n+2) + Fibonacci(2*n+2): n in [0..30]]; // _G. C. Greubel_, Apr 09 2021

%o (Sage) [2*n*lucas_number2(2*n+2,1,-1) + fibonacci(2*n+2) for n in (0..30)] # _G. C. Greubel_, Apr 09 2021

%Y Cf. A000032, A000045, A001871, A001906, A002878, A060923, A061186.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Apr 20 2001