A178510 -id:A178510 - cp's OEIS frontend

A178512 Reversed decimal expansions of A178510.

1, 121, 14521, 1742521, 209102521, 25092302521, 3011076302521, 361329156302521, 43359498756302521, 5203139850756302521, 624376782090756302521, 74925213850890756302521, 8991025662106890756302521, 1078923079452826890756302521, 129470769534339226890756302521

Offset: 1

Mark Dols, May 29 2010

Related to backward decimal expansion of fraction 1/119 and Pell numbers. [How? - Joerg Arndt, May 14 2011]

Vincenzo Librandi, Table of n, a(n) for n = 1..150
Index entries for linear recurrences with constant coefficients, signature (121,-120).

Cf. A000129, A021083, A038207, A178510, A178511.

[(1/119)*(120^n-1): n in [1..20]]; // Vincenzo Librandi, May 17 2011

NestList[120#+1&,1,20] (* Harvey P. Dale, May 21 2023 *)

Vec(x/((x-1)*(120*x-1)) + O(x^20)) \\ Colin Barker, Oct 02 2015

a(n) = 120*a(n-1) + 1.
From Colin Barker, Oct 02 2015: (Start)
a(n) = 121*a(n-1) - 120*a(n-2) for n > 2.
G.f.: x / ((x-1)*(120*x-1)).
(End)

A178511 a(n) = (1/119)*(100^n -(-19)^n).

Original entry on oeis.org

1, 81, 8461, 839241, 84054421, 8402966001, 840343645981, 84033470726361, 8403364056199141, 840336082932216321, 84033614424287889901, 8403361325938530091881, 840336134807167928254261, 84033613438663809363169041, 8403361344665387622099788221

Offset: 1

Mark Dols, May 29 2010

Numerators in alternating Sum_{n>=0} 19^n/100^(n+1).

Related to decimal expansion of fraction of 1/119 and Pell numbers. [In which way? - Joerg Arndt, May 14 2011]

Vincenzo Librandi, Table of n, a(n) for n = 1..150
Index entries for linear recurrences with constant coefficients, signature (81,1900).

Cf. A000129, A021083, A038207, A178510.

[(1/119)*(100^n -(-19)^n): n in [1..20]]; // Vincenzo Librandi, May 17 2011

LinearRecurrence[{81,1900},{1,81},20] (* Harvey P. Dale, Nov 12 2022 *)

Vec(-x/((19*x+1)*(100*x-1)) + O(x^20)) \\ Colin Barker, Oct 02 2015

a(n+1) = a(n)*100 +- 19^n with a(0)=0 and a(1)= 1.
From Colin Barker, Oct 02 2015: (Start)
a(n) = 81*a(n-1) + 1900*a(n-2) for n > 2.
G.f.: -x / ((19*x+1)*(100*x-1)).
(End)

A178513 Partial sums of 80^n.

Original entry on oeis.org

1, 81, 6481, 518481, 41478481, 3318278481, 265462278481, 21236982278481, 1698958582278481, 135916686582278481, 10873334926582278481, 869866794126582278481, 69589343530126582278481, 5567147482410126582278481, 445371798592810126582278481

Offset: 0

Mark Dols, May 29 2010

Related to backward decimal expansion of fraction 1/79 and Pell numbers. [In which way? - Joerg Arndt, May 17 2011]

Vincenzo Librandi, Table of n, a(n) for n = 0..150
Index entries for linear recurrences with constant coefficients, signature (81,-80).

Cf. A000129, A021083, A038207, A178510, A178511, A178512.

Accumulate[80^Range[0,20]] (* Harvey P. Dale, Aug 11 2014 *)

a(n) = 80*a(n-1) + 1.
a(n) = (80^(n+1)-1)/79.
G.f.: 1/((1-80*x)*(1-x)).

cp's OEIS Frontend

A178512 Reversed decimal expansions of A178510.

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A178511 a(n) = (1/119)*(100^n -(-19)^n).

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A178513 Partial sums of 80^n.

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