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URL: https://oeis.org/A137215

⇱ A137215 - OEIS

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A137215
a(n) = 3*(10^n) + (n^2 + 1)*(10^n - 1)/9.
1
3, 32, 355, 4110, 48887, 588886, 7111107, 85555550, 1022222215, 12111111102, 142222222211, 1655555555542, 19111111111095, 218888888888870, 2488888888888867, 28111111111111086, 315555555555555527, 3522222222222222190, 39111111111111111075, 432222222222222222182
OFFSET
0,1
COMMENTS
Sequence generalized: a(n) = a(0)*(B^n) + F(n)* ((B^n)-1)/(B-1); a(0), B integers, F(n) arithmetic function.
Examples:
a(0) = 1, B = 10, F(n) = 1 gives A002275, F(n) = 2 gives A090843, F(n) = 3 gives A097166, F(n) = 4 gives A099914, F(n) = 5 gives A099915.
a(0) = 1, B = 2, F(n) = 1 gives A000225, F(n) = 2 gives A033484, F(n) = 3 gives A036563, F(n) = 4 gives A048487, F(n) = 5 gives A048488, F(n) = 6 gives A048489.
a(0) = 1, B = 3, F(n) = 1 gives A003462, F(n) = 2 gives A048473, F(n) = 3 gives A134931, F(n) = 4 gives A058481, F(n) = 5 gives A116952.
a(0) = 1, B = 4, F(n) = 1 gives A002450, F(n) = 2 gives A020989, F(n) = 3 gives A083420, F(n) = 4 gives A083597, F(n) = 5 gives A083584.
a(0) = 1, B = 5, F(n) = 1 gives A003463, F(n) = 2 gives A057651, F(n) = 3 gives A117617, F(n) = 4 gives A081655.
a(0) = 2, B = 10, F(n) = 1 gives A037559, F(n) = 2 gives A002276.
LINKS
FORMULA
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
EXAMPLE
a(3) = 3*10^3 + (3*3 + 1)*(10^3 - 1)/9 = 4110.
MATHEMATICA
Table[3*10^n +(n^2 +1)*(10^n -1)/9, {n, 0, 30}] (* G. C. Greubel, Jan 05 2022 *)
PROG
(PARI) a(n) = 3*(10^n) + (n*n+1)*((10^n)-1)/9; \\ Jinyuan Wang, Feb 27 2020
(SageMath) [3*10^n +(1+n^2)*(10^n -1)/9 for n in (0..30)] # G. C. Greubel, Jan 05 2022
CROSSREFS
Sequence in context: A037799 A091706 A091705 * A300366 A231591 A123336
KEYWORD
nonn,easy
AUTHOR
Ctibor O. Zizka, Mar 06 2008
EXTENSIONS
More terms from R. J. Mathar, Mar 16 2008
More terms from Jinyuan Wang, Feb 27 2020
STATUS
approved