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A086576
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a(n) = 5*(10^n - 1).
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8
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0, 45, 495, 4995, 49995, 499995, 4999995, 49999995, 499999995, 4999999995, 49999999995, 499999999995, 4999999999995, 49999999999995, 499999999999995, 4999999999999995, 49999999999999995, 499999999999999995, 4999999999999999995, 49999999999999999995, 499999999999999999995
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OFFSET
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0,2
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COMMENTS
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Original definition: a(n) = k where R(k+5) = 5.
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LINKS
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FORMULA
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a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 45*x/((1 - x)*(1 - 10*x)). (End)
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EXAMPLE
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1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45;
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495;
111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999 = 4995;
1111 + 2222 + 3333 + 4444 + 5555 + 6666 + 7777 + 8888 + 9999 = 49995;
11111 + 22222 + 33333 + 44444 + 55555 + 66666 + 77777 + 88888 + 99999 = 499995; etc. (End)
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MATHEMATICA
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Join[{0}, LinearRecurrence[{11, -10}, {45, 495}, 50]] (* G. C. Greubel, Jul 08 2016 *)
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CROSSREFS
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One of family of sequences of form a(n)=k, where R(k+m)=m, m = 1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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