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A137215
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a(n) = 3*(10^n) + (n^2 + 1)*(10^n - 1)/9.
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1
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3, 32, 355, 4110, 48887, 588886, 7111107, 85555550, 1022222215, 12111111102, 142222222211, 1655555555542, 19111111111095, 218888888888870, 2488888888888867, 28111111111111086, 315555555555555527, 3522222222222222190, 39111111111111111075, 432222222222222222182
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OFFSET
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0,1
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COMMENTS
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Sequence generalized: a(n) = a(0)*(B^n) + F(n)* ((B^n)-1)/(B-1); a(0), B integers, F(n) arithmetic function.
Examples:
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LINKS
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FORMULA
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a(n) = 3*(10^n) + (n^2 + 1)*(10^n - 1)/9.
O.g.f.: (3 - 67*x + 478*x^2 - 1002*x^3 + 850*x^4 - 100*x^5)/((1-x)^3 * (1-10*x)^3). - R. J. Mathar, Mar 16 2008
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EXAMPLE
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a(3) = 3*10^3 + (3*3 + 1)*(10^3 - 1)/9 = 4110.
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MATHEMATICA
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Table[3*10^n +(n^2 +1)*(10^n -1)/9, {n, 0, 30}] (* G. C. Greubel, Jan 05 2022 *)
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PROG
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(PARI) a(n) = 3*(10^n) + (n*n+1)*((10^n)-1)/9; \\ Jinyuan Wang, Feb 27 2020
(Sage) [3*10^n +(1+n^2)*(10^n -1)/9 for n in (0..30)] # G. C. Greubel, Jan 05 2022
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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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EXTENSIONS
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STATUS
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approved
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