A060934 Second column of Lucas bisection triangle (even part).

1, 17, 80, 303, 1039, 3364, 10493, 31885, 95032, 279051, 809771, 2327372, 6636025, 18794633, 52925984, 148303719, 413768263, 1150029940, 3185625077, 8797726981, 24230897416, 66574108227

Offset

0,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

É. Czabarka, R. Flórez, and L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

Formula

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

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

a(n) = 2*n*Lucas(2*n+2) + Fibonacci(2*n+2). - G. C. Greubel, Apr 09 2021

Mathematica

LinearRecurrence[{6, -11, 6, -1}, {1, 17, 80, 303}, 31] (* G. C. Greubel, Apr 09 2021 *)
CoefficientList[Series[(1+11x-11x^2+4x^3)/(1-3x+x^2)^2, {x, 0, 30}], x] (* Harvey P. Dale, Aug 28 2021 *)

Prog

(Magma) [2*n*Lucas(2*n+2) + Fibonacci(2*n+2): n in [0..30]]; // G. C. Greubel, Apr 09 2021
(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

Crossrefs

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

Sequence in context: A353937 A172045 A338549 * A228602 A100688 A044204

Adjacent sequences: A060931 A060932 A060933 * A060935 A060936 A060937

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 20 2001

Status

approved