The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A060934

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A060934

Second column of Lucas bisection triangle (even part).
(history; published version)

#17 by Harvey P. Dale at Sat Aug 28 18:31:59 EDT 2021

STATUS

editing

approved

#16 by Harvey P. Dale at Sat Aug 28 18:31:55 EDT 2021

MATHEMATICA

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

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approved

editing

#15 by N. J. A. Sloane at Fri Apr 09 09:15:38 EDT 2021

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proposed

approved

#14 by Michel Marcus at Fri Apr 09 02:39:26 EDT 2021

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editing

proposed

#13 by Michel Marcus at Fri Apr 09 02:39:18 EDT 2021

LINKS

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.

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proposed

editing

#12 by Jon E. Schoenfield at Fri Apr 09 01:09:06 EDT 2021

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editing

proposed

#11 by Jon E. Schoenfield at Fri Apr 09 01:09:04 EDT 2021

FORMULA

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

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proposed

editing

#10 by G. C. Greubel at Fri Apr 09 01:04:02 EDT 2021

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editing

proposed

#9 by G. C. Greubel at Fri Apr 09 00:53:18 EDT 2021

COMMENTS

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

LINKS

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

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

FORMULA

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 *)

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

A002878(n)=A060923(n, 0).

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

STATUS

approved

editing

#8 by Joerg Arndt at Sat Jun 23 02:32:41 EDT 2018

STATUS

proposed

approved