The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A180666 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A180666

Golden Triangle sums: a(n)=a(n-4)+A001654(n) with a(0)=0, a(1)=1, a(2)=2 and a(3)=6.
(history; published version)

#13 by Joerg Arndt at Mon Oct 14 05:52:19 EDT 2024

STATUS

proposed

approved

#12 by Jason Yuen at Mon Oct 14 04:30:47 EDT 2024

STATUS

editing

proposed

#11 by Jason Yuen at Mon Oct 14 04:29:33 EDT 2024

FORMULA

a(n) = addSum_{k=0..floor(n/4)} A180662(n-3*k,n-4*k),k=0..floor(n/4)),n=0..nmax).

STATUS

approved

editing

#10 by N. J. A. Sloane at Thu Aug 18 09:50:36 EDT 2016

STATUS

editing

approved

#9 by N. J. A. Sloane at Thu Aug 18 09:50:20 EDT 2016

MAPLE

nmax:=27: with(combinat): for n from 0 to nmax do A001654(n):=fibonacci(n)*fibonacci(n+1) od: a(0):=0: a(1):=1: a(2):=2: a(3):=6: for n from 4 to nmax do a(n):=a(n-4)+A001654(n) od: seq(a(n), n=0..nmax);

STATUS

proposed

editing

Discussion

Thu Aug 18

09:50

N. J. A. Sloane: I restored the old Maple program

#8 by Michael De Vlieger at Thu Aug 18 08:24:52 EDT 2016

STATUS

editing

proposed

Discussion

Thu Aug 18

09:36

Joerg Arndt: I tend to agree with Alois.  At the very least nothing seems wrong with the old code, so it should not be deleted.

#7 by Michael De Vlieger at Thu Aug 18 08:24:43 EDT 2016

MATHEMATICA

Take[Total@{#, PadLeft[Drop[#, -4], Length@ #]}, Length@ # - 4] &@ Table[Times @@ Fibonacci@ {n, n + 1}, {n, 0, 31}] (* or *)

CoefficientList[Series[(-x)/((x^2 - 3 x + 1) (x - 1) (x + 1)^2 (x^2 + 1)), {x, 0, 27}], x] (* Michael De Vlieger, Aug 18 2016 *)

STATUS

proposed

editing

#6 by Michel Marcus at Thu Aug 18 07:33:23 EDT 2016

STATUS

editing

proposed

Discussion

Thu Aug 18

07:57

Alois P. Heinz: The old program was correct and it was self-contained.  You replaced it by a program that is not self-contained.

08:08

R. J. Mathar: Self-containment is futile. Code re-use is much more important.

#5 by Michel Marcus at Thu Aug 18 07:33:17 EDT 2016

FORMULA

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

STATUS

proposed

editing

#4 by R. J. Mathar at Thu Aug 18 07:20:03 EDT 2016

STATUS

editing

proposed