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A060934 Second column of Lucas bisection triangle (even part). 4
1, 17, 80, 303, 1039, 3364, 10493, 31885, 95032, 279051, 809771, 2327372, 6636025, 18794633, 52925984, 148303719, 413768263, 1150029940, 3185625077, 8797726981, 24230897416, 66574108227 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Numerator of g.f. is row polynomial Sum_{m=0..3} A061186(2, m)*x^m.
LINKS
É. Czabarka, R. Flórez, and L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.
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
Sequence in context: A353937 A172045 A338549 * A228602 A100688 A044204
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 20 2001
STATUS
approved

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Last modified April 22 08:30 EDT 2024. Contains 371893 sequences. (Running on oeis4.)