A165511 a(0)=1, a(1)=10, a(n) = 90*a(n-2) - a(n-1).
1, 10, 80, 820, 6380, 67420, 506780, 5561020, 40049180, 460442620, 3143983580, 38295852220, 244662669980, 3201964029820, 18817676268380, 269359086415420, 1424231777738780, 22818085999649020, 105362773996841180
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..998 (terms 0..100 from Franklin T. Adams-Watters)
- Index entries for linear recurrences with constant coefficients, signature (-1, 90).
Programs
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Magma
[(20*9^n-(-10)^n)/19: n in [0..50]]; // G. C. Greubel, Oct 21 2018
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Mathematica
LinearRecurrence[{-1,90},{1,10},20] (* or *) CoefficientList[Series[ (1+11x)/(1+x-90x^2),{x,0,20}],x] (* Harvey P. Dale, Apr 30 2011 *) -
PARI
vector(50, n, n--; (20*9^n-(-10)^n)/19) \\ G. C. Greubel, Oct 21 2018
Formula
G.f.: (1+11*x)/(1+x-90*x^2).
a(n) = Sum_{k=0..n} A112555(n,k)*9^k.
a(n) = (20*9^n-(-10)^n)/19. - Klaus Brockhaus, Sep 26 2009
E.g.f.: (20*exp(9*x) - exp(-10*x))/19. - G. C. Greubel, Oct 21 2018
Comments