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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A117088 a(n) = (11*5^n - 7)/4.

Original entry on oeis.org

1, 12, 67, 342, 1717, 8592, 42967, 214842, 1074217, 5371092, 26855467, 134277342, 671386717, 3356933592, 16784667967, 83923339842, 419616699217, 2098083496092, 10490417480467, 52452087402342, 262260437011717, 1311302185058592, 6556510925292967
Offset: 0

Views

Author

Parthasarathy Nambi, Apr 17 2006

Keywords

Examples

			If n=1 then 5*(n-1) + 7 = 5*1 + 7 = 12, which is the second term.

Links

Crossrefs

Cf. A117617, A116952.

Programs

Formula

a(n) = 5*a(n-1) + 7 with a(0) = 1.
G.f.: (1+6*x)/((1-x)*(1-5*x)). - Philippe Deléham, Feb 22 2014
a(n) = 6*a(n-1) - 5*a(n-2), a(0) = 1, a(1) = 12. - Philippe Deléham, Feb 22 2014
a(n) = (11*5^n - 7) / 4. - Ralf Stephan, Feb 23 2014

Extensions

Definition corrected and better name by Ralf Stephan, Feb 23 2014

A137215 a(n) = 3*(10^n) + (n^2 + 1)*(10^n - 1)/9.

Original entry on oeis.org

3, 32, 355, 4110, 48887, 588886, 7111107, 85555550, 1022222215, 12111111102, 142222222211, 1655555555542, 19111111111095, 218888888888870, 2488888888888867, 28111111111111086, 315555555555555527, 3522222222222222190, 39111111111111111075, 432222222222222222182
Offset: 0

Views

Author

Ctibor O. Zizka, Mar 06 2008

Keywords

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.

Examples

			a(3) = 3*10^3 + (3*3 + 1)*(10^3 - 1)/9 = 4110.

Links

Crossrefs

Cf. A002275, A011557.

Programs

  • Mathematica
    Table[3*10^n +(n^2 +1)*(10^n -1)/9, {n,0,30}] (* G. C. Greubel, Jan 05 2022 *)
  • 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

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

Extensions

More terms from R. J. Mathar, Mar 16 2008
More terms from Jinyuan Wang, Feb 27 2020
Showing 1-2 of 2 results.

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