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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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A187709 a(n) = (7*9^n + 1)/8.

Original entry on oeis.org

1, 8, 71, 638, 5741, 51668, 465011, 4185098, 37665881, 338992928, 3050936351, 27458427158, 247125844421, 2224132599788, 20017193398091, 180154740582818, 1621392665245361, 14592533987208248, 131332805884874231, 1181995252963868078, 10637957276674812701, 95741615490073314308, 861674539410659828771
Offset: 0

Views

Author

Sture Sjöstedt, Mar 30 2011

Keywords

Comments

Case r=9 in a(n)=((r-2)*r^n+1)/(r-1).

Links

Crossrefs

Cf. A007051, A083068, A270472 (first differences), A059482: cases r=3,8,10 in ((r-2)*r^n+1)/(r-1), respectively.

Programs

Formula

a(n) = (7*9^n + 1)/8.
a(n) = +10*a(n-1) -9*a(n-2).
a(n) = 8*Sum_{i=0..n-1} a(i) -n + 1.
G.f.: (1-2*x)/((1-x)*(1-9*x)).
a(n) = 9^n - Sum_{i=0..n-1} 9^i for n>0. - Bruno Berselli, Jun 20 2013
E.g.f.: (7*exp(9*x) + exp(x))/8. - G. C. Greubel, Nov 06 2018

Extensions

Additional formulas from Bruno Berselli

A270369 Expansion of g.f. (1-7*x)/(1-9*x).

Original entry on oeis.org

1, 2, 18, 162, 1458, 13122, 118098, 1062882, 9565938, 86093442, 774840978, 6973568802, 62762119218, 564859072962, 5083731656658, 45753584909922, 411782264189298, 3706040377703682, 33354363399333138, 300189270593998242, 2701703435345984178, 24315330918113857602, 218837978263024718418
Offset: 0

Views

Author

Colin Barker, Mar 18 2016

Keywords

Links

Crossrefs

Cf. A001019 (powers of 9), A054879 (partial sums), A132025.
Cf. similar sequences with g.f. (1-k*x)/(1-9*x) and k=0..8: A001019 (k=0; k=8 gives two initial 1's ), A055275 (k=1), A270472 (k=2), A092810 (k=3), A067403 (k=4), A270473 (k=5), A102518 (k=6), this sequence (k=7).

Programs

  • Mathematica
    CoefficientList[Series[(1-7x)/(1-9x),{x,0,20}],x] (* or *) Join[ {1}, NestList[9#&,2,20]] (* Harvey P. Dale, Oct 15 2017 *)
  • PARI
    Vec((1-7*x)/(1-9*x) + O(x^30))

Formula

G.f.: (1-7*x)/(1-9*x).
a(n) = 9*a(n-1) for n>1.
a(n) = 2*9^(n-1) for n>0.
From Amiram Eldar, May 08 2023: (Start)
Sum_{n>=0} 1/a(n) = 25/16.
Sum_{n>=0} (-1)^n/a(n) = 11/20.
Product_{n>=1} (1 - 1/a(n)) = A132025. (End)
E.g.f.: (2*exp(9*x) + 7)/9. - Elmo R. Oliveira, Mar 25 2025
Showing 1-2 of 2 results.

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