A178511 -id:A178511 - 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)

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)).

A178643 Square array read by antidiagonals. Convolution of a(n) = 2*a(n-1) - a(n-2) and 10^n.

Original entry on oeis.org

1, 10, 2, 100, 19, 4, 1000, 190, 36, 8, 10000, 1900, 361, 68, 16, 100000, 19000, 3610, 686, 128, 32, 1000000, 190000, 36100, 6859, 1304, 240, 64, 10000000, 1900000, 361000, 68590, 13032, 2480, 448, 128, 100000000, 19000000, 3610000, 685900, 130321, 24760, 4720, 832, 256

Offset: 1

Mark Dols, May 31 2010

Diagonals sum up to A014824.

Alternating diagonal sum gives decimal expansion of fraction 1/119 (A021123).

			Array starts:
     1,    2,    4,    8,
    10,   19,   36,   68,
   100,  190,  361,  686,
  1000, 1900, 3610, 6859,

Robin Visser, Table of n, a(n) for n = 1..10000

Cf. A014824, A000129, A021123, A021083, A178511.

def a(n,k):
    T = [[0 for j in range(k+1)] for i in range(n+1)]
    for i in range(n+1): T[i][0] = 10^i
    for j in range(1, k+1):
        T[0][j] = 2^j
        for i in range(1, n+1): T[i][j] = 2*T[i][j-1] - T[i-1][j-1]
    return T[n][k]  # Robin Visser, Aug 09 2023

T(n,k) = 2*T(n,k-1) - T(n-1,k-1) for all n, k > 0, where T(n,0) = 10^n and T(0,k) = 2^k. - Robin Visser, Aug 09 2023

More terms from Robin Visser, Aug 09 2023

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A178512 Reversed decimal expansions of A178510.

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A178513 Partial sums of 80^n.

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A178643 Square array read by antidiagonals. Convolution of a(n) = 2*a(n-1) - a(n-2) and 10^n.

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