The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A356829 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A356829

Number of vertex cuts in the n-Möbius ladder.
(history; published version)

#15 by Charles R Greathouse IV at Sat Apr 22 00:47:09 EDT 2023

STATUS

editing

approved

#14 by Charles R Greathouse IV at Sat Apr 22 00:47:06 EDT 2023

LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,48,-11,-22,7,4).

STATUS

approved

editing

#13 by Michael De Vlieger at Wed Aug 31 23:06:43 EDT 2022

STATUS

proposed

approved

#12 by Eric W. Weisstein at Wed Aug 31 22:11:35 EDT 2022

STATUS

editing

proposed

#11 by Eric W. Weisstein at Wed Aug 31 22:11:24 EDT 2022

DATA

0, 0, 8, 82, 512, 2644, 12364, 54598, 232772, 970520, 3988624, 16239066, 65709256, 264814140, 1064414100, 4271035662, 17118683020, 68563527616, 274481537112, 1098506723042, 4395504614544, 17585769696164, 70352578566620, 281434319454038, 1125797816327892

OFFSET

3,1

1,3

COMMENTS

Sequence extended to n = 1 using formula.

LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,48,-11,-22,7,4).

FORMULA

a(n) = 4^n + n - LucasL(n, 2) - 3*n*Fibonacci(n, 2).

a(n) = 10*a(n-1) - 35*a(n-2) + 48*a(n-3) - 11*a(n-4) - 22*a(n-5) + 7*a(n-6) + 4*a(n-7).

G.f.: 2*x^3*(-4-x+14*x^2-5*x^3+2*x^4)/((-1+x)^2*(-1+4*x)*(-1+2*x+x^2)^2).

MATHEMATICA

Table[4^n + n - LucasL[n, 2] - 3 n Fibonacci[n, 2], {n, 20}]

LinearRecurrence[{10, -35, 48, -11, -22, 7, 4}, {0, 0, 8, 82, 512, 2644, 12364}, 20]

CoefficientList[Series[2 x^2 (-4 - x + 14 x^2 - 5 x^3 + 2 x^4)/((-1 + x)^2 (-1 + 4 x) (-1 + 2 x + x^2)^2), {x, 0, 20}], x]

STATUS

approved

editing

#10 by Joerg Arndt at Tue Aug 30 11:20:37 EDT 2022

STATUS

editing

approved

#9 by Joerg Arndt at Tue Aug 30 11:20:28 EDT 2022

FORMULA

a(n) = 2^(2*n) - A286185(n) - 1. - Pontus von Brömssen, Aug 30 2022

STATUS

proposed

editing

#8 by Pontus von Brömssen at Tue Aug 30 11:18:59 EDT 2022

STATUS

editing

proposed

#7 by Pontus von Brömssen at Tue Aug 30 11:18:52 EDT 2022

KEYWORD

nonn,more,new

STATUS

proposed

editing

#6 by Pontus von Brömssen at Tue Aug 30 11:10:51 EDT 2022

STATUS

editing

proposed