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A232999 a(n) = 6 + 4*(-1)^n + (2+sqrt(3))^n + (2-sqrt(3))^n + 2*(1+sqrt(2))^n + 2*(1-sqrt(2))^n. 1
16, 10, 36, 82, 272, 890, 3108, 11042, 39952, 146026, 537636, 1988722, 7379216, 27436250, 102144036, 380604482, 1418981392, 5292200650, 19742287908, 73658763922, 274848860432, 1025630676026, 3827417932836, 14283423231842, 53304783436816, 198932109576490, 742414961433636, 2770706748348082 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
D. Deford, Seating rearrangements on arbitrary graphs, preprint 2013, Involve, Volume 7, Number 6 (2014), 787-805. See Table 2.
FORMULA
G.f.: -2*(x^5+16*x^4-32*x^3-44*x^2+43*x-8) / ((x-1)*(x+1)*(x^2-4*x+1)*(x^2+2*x-1)). - Colin Barker, Sep 12 2014
a(n) = 6*a(n-1) - 7*a(n-2) - 8*a(n-3) + 9*a(n-4) + 2*a(n-5) - a(n-6) for n >= 6. - Nathaniel Johnston, Sep 12 2014
E.g.f.: 4*exp(-x) + 6*exp(x) + 2*exp((1 + sqrt(2))*x) + exp(-(-2 + sqrt(3))*x) + exp((2 + sqrt(3))*x) + 2*exp(x - sqrt(2)*x). - Stefano Spezia, Oct 07 2018
MAPLE
f:=n->expand(6+4*(-1)^n
+(2+sqrt(3))^n
+(2-sqrt(3))^n
+2*(1+sqrt(2))^n
+2*(1-sqrt(2))^n);
[seq(f(n), n=0..30)];
MATHEMATICA
LinearRecurrence[{6, -7, -8, 9, 2, -1}, {16, 10, 36, 82, 272, 890}, 30] (* Harvey P. Dale, Mar 10 2015 *)
Simplify[CoefficientList[Series[4 E^-x + 6 E^x + 2 E^((1 + Sqrt[2]) x) + E^(-(-2 + Sqrt[3]) x) + E^((2 + Sqrt[3]) x) + 2 E^(x - Sqrt[2] x), {x, 0, 20}], x]*Table[k!, {k, 0, 30}]] (* Stefano Spezia, Oct 07 2018 *)
PROG
(PARI) Vec(-2*(x^5+16*x^4-32*x^3-44*x^2+43*x-8)/((x-1)*(x+1)*(x^2-4*x+1)*(x^2+2*x-1)) + O(x^100)) \\ Colin Barker, Sep 12 2014
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(-2*(x^5+16*x^4-32*x^3-44*x^2+43*x-8)/((x-1)*(x+1)*(x^2-4*x+1)*(x^2+2*x-1)))); // G. C. Greubel, Oct 06 2018
(GAP) a:=[16, 10, 36, 82, 272, 890];; for n in [7..30] do a[n]:=6*a[n-1]-7*a[n-2]-8*a[n-3]+9*a[n-4]+2*a[n-5]-a[n-6]; od; a; # Muniru A Asiru, Oct 07 2018
CROSSREFS
Sequence in context: A154615 A040242 A306378 * A217157 A070578 A225842
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 17 2013
STATUS
approved

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Last modified July 13 17:31 EDT 2024. Contains 374284 sequences. (Running on oeis4.)