A108896 Numbers whose outer two digits are 9's and inner digits are 4's.
949, 9449, 94449, 944449, 9444449, 94444449, 944444449, 9444444449, 94444444449, 944444444449, 9444444444449, 94444444444449, 944444444444449, 9444444444444449, 94444444444444449, 944444444444444449, 9444444444444444449, 94444444444444444449
Offset: 1
Links
- Cino Hilliard, Proof 94..49
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Programs
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Mathematica
Table[10*FromDigits[PadRight[{9},n,4]]+9,{n,2,20}] (* Harvey P. Dale, Apr 02 2018 *) -
PARI
S(n,r,m)=for(x=1,n,y=m*10^(x+1)+m+r*10*(10^x-1)/9;print1(y","))
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Python
def a(n): return int('9' + '4'*n + '9') print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Jul 26 2022
Formula
a(n) = 9*10^(n+1) + 9 + 40*(10^n-1)/9.
From Chai Wah Wu, Jul 27 2022: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2.
G.f.: x*(949 - 990*x)/((x - 1)*(10*x - 1)). (End)
Comments