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Revision History for A109794

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A109794

a(2n) = A001906(n+1), a(2n+1) = A002878(n).
(history; published version)

#43 by Michael De Vlieger at Wed Mar 13 21:51:48 EDT 2024

STATUS

proposed

approved

#42 by Robert C. Lyons at Wed Mar 13 17:43:19 EDT 2024

STATUS

editing

proposed

#41 by Robert C. Lyons at Wed Mar 13 17:43:17 EDT 2024

COMMENTS

Floretion Algebra Multiplication Program, FAMP code: 4jesleftforsumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], vesleftforsumseq = A000045, sumtype: (Y[15], *, inty*sum) (internal program code)

PROG

STATUS

approved

editing

#40 by Harvey P. Dale at Tue Aug 10 17:57:47 EDT 2021

STATUS

editing

approved

#39 by Harvey P. Dale at Tue Aug 10 17:57:44 EDT 2021

MATHEMATICA

CoefficientList[Series[(1+x+x^3)/((1+x-x^2)(1-x-x^2)), {x, 0, 40}], x] (* Harvey P. Dale, Aug 10 2021 *)

STATUS

approved

editing

#38 by Alois P. Heinz at Sun Aug 26 21:03:00 EDT 2018

STATUS

editing

approved

#37 by Alois P. Heinz at Sun Aug 26 21:02:55 EDT 2018

MAPLE

seq (a(n), n=0..50); # Alois P. Heinz, May 02 2011

STATUS

proposed

editing

#36 by Joerg Arndt at Sun Aug 26 05:03:43 EDT 2018

STATUS

editing

proposed

#35 by Joerg Arndt at Sun Aug 26 05:03:28 EDT 2018

FORMULA

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

MATHEMATICA

s = Sqrt[5]; a[n_] := Simplify[( 3s/20 + 3/4) (1/2 + s/2)^n + (-3s/20 + 3/4) (1/2 - s/2)^n + (-3s/20 - 1/4) (-1/2 + s/2)^ n + (3s/20 - 1/4) (-1/2 - s/2)^n]; Array[a, 40, 0] (* or *)CoefficientList[ Series[(x^3 + x + 1)/(x^4 - 3 x^2 + 1), {x, 0, 40}], x] (* or *)LinearRecurrence[{0, 3, 0, -1}, {1, 1, 3, 4}, 40] (* Robert G. Wilson v, Aug 06 2018 *)

LinearRecurrence[{0, 3, 0, -1}, {1, 1, 3, 4}, 40] (* Robert G. Wilson v, Aug 06 2018 *)

STATUS

proposed

editing

Discussion

Sun Aug 26

05:03

Joerg Arndt: Like this.

#34 by Daniel Forgues at Sat Aug 25 22:09:56 EDT 2018

STATUS

editing

proposed