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A032343
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a(n) = 10*a(n-1)+n^2, a(0)=0.
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1
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0, 1, 14, 149, 1506, 15085, 150886, 1508909, 15089154, 150891621, 1508916310, 15089163221, 150891632354, 1508916323709, 15089163237286, 150891632373085, 1508916323731106, 15089163237311349, 150891632373113814
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OFFSET
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0,3
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COMMENTS
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a(n)/10^n converges to 110/729=0.15089163237311...
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LINKS
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FORMULA
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a(n) =(10^n-1)*(110/729)-n^2/9-n*(20/81).
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MATHEMATICA
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CoefficientList[Series[(x^2+x)/((x-1)^3 (10x-1)), {x, 0, 30}], x] (* Harvey P. Dale, Mar 20 2011 *)
RecurrenceTable[{a[0] == 0, a[n] == 10*a[n-1] + n^2}, a, {n, 100}] (* Vincenzo Librandi, Mar 10 2013 *)
LinearRecurrence[{13, -33, 31, -10}, {0, 1, 14, 149}, 20] (* Harvey P. Dale, May 25 2024 *)
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PROG
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(Magma) [0] cat [n le 1 select n else 10*Self(n-1)+n^2: n in [1..20]]; // Vincenzo Librandi, Mar 10 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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