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Revision History for A123012
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
MATHEMATICA
Join[{a=1, b=2}, Table[c=2*b+21*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
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LINKS
<a href="/index/Rec#order_02">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (2,21).
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NAME
G.f.: Expansion of 1/(1 - 2*x - 21*x^2).
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NAME
G.f.: 1/(1 - 2*x - 21*x^2).
FORMULA
a(0)=1, a(1)=2, a(n) = 2*a(n-1) + 21*a(n-2) for n>1. [_- _Philippe Deléham_, Sep 19 2009]
a(n) = (1/2 + sqrt(22)/44)*(1 + sqrt(22))^n + (1/2 - sqrt(22)/44)*(1 - sqrt(22))^n. - Antonio Alberto Olivares, Jun 08 2011
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MAPLE
A:= gfun:-rectoproc({a(n)=2*a(n-1)+21*a(n-2), a(0)=1, a(1)=2}, a(n), remember):
map(A, [$0..30]); # Robert Israel, Jan 28 2015
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