The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A089076

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A089076

Expansion of -x - x^3*(2 -2*x^4 +x^5)/((1-x^2)*(1+x+x^4)).
(history; published version)

#21 by Joerg Arndt at Sat Dec 24 02:35:56 EST 2022

STATUS

editing

approved

#20 by Joerg Arndt at Sat Dec 24 02:34:25 EST 2022

MATHEMATICA

(* First program *)

digits=100; NSolve[x^4 -x^3 -1==0, x]; k = 1.38028; q = N[k -1/k^3, 20];

m0 = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, -q}};

m[n_] = MatrixPower[m0, n];

Join[{-1, 0}, Table[Floor[Re[m[n][[4, 4]]]], {n, 3, digits}]]

(* Second program *)

STATUS

approved

editing

#19 by Harvey P. Dale at Wed Aug 11 17:07:28 EDT 2021

STATUS

editing

approved

#18 by Harvey P. Dale at Wed Aug 11 17:07:25 EDT 2021

MATHEMATICA

LinearRecurrence[{-1, 1, 1, 1, 0, -1}, {-1, 0, -2, 2, -4, 4, -6, 7}, 50] (* Harvey P. Dale, Aug 11 2021 *)

STATUS

approved

editing

#17 by N. J. A. Sloane at Fri Feb 19 18:34:03 EST 2021

STATUS

proposed

approved

#16 by G. C. Greubel at Fri Feb 19 14:17:56 EST 2021

STATUS

editing

proposed

#15 by G. C. Greubel at Fri Feb 19 14:17:25 EST 2021

MATHEMATICA

(* First program *)

digits=100; NSolve[x^4 -x^3 -1==0, x]; k = 1.38028; q = N[k -1/k^3, 20];

m0 = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, -q}};

m[n_] = MatrixPower[m0, n];

Join[{-1, 0}, Table[Floor[Re[m[n][[4, 4]]]], {n, 3, digits}]]

(* Second program *)

STATUS

proposed

editing

Discussion

Fri Feb 19

14:17

G. C. Greubel: Fixed original Mathematica program.

#14 by G. C. Greubel at Fri Feb 19 14:08:48 EST 2021

STATUS

editing

proposed

#13 by G. C. Greubel at Fri Feb 19 14:08:32 EST 2021

CROSSREFS

Cf. A089074, A089075, A089077.

STATUS

proposed

editing

#12 by G. C. Greubel at Fri Feb 19 14:04:58 EST 2021

STATUS

editing

proposed