A247841 a(n) = Sum_{k=2..n} 8^k.

0, 64, 576, 4672, 37440, 299584, 2396736, 19173952, 153391680, 1227133504, 9817068096, 78536544832, 628292358720, 5026338869824, 40210710958656, 321685687669312, 2573485501354560, 20587884010836544, 164703072086692416, 1317624576693539392

Offset: 1

Author

Vincenzo Librandi, Sep 25 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. similar sequences listed in A247817.

Cf. A052379.

Programs

Magma

[0] cat [&+[8^k: k in [2..n]]: n in [2..30]];

Magma

[(8^(n+1)-64)/7: n in [1..30]];

Mathematica

RecurrenceTable[{a[1] == 0, a[n] == a[n-1] + 8^n}, a, {n, 30}] (* or *) CoefficientList[Series[64 x / ((1 - x) (1 - 8 x)), {x, 0, 30}], x]
LinearRecurrence[{9,-8},{0,64},30] (* Harvey P. Dale, May 01 2018 *)

Formula

G.f.: 64*x^2/((1-x)*(1-8*x)).

a(n) = a(n-1) + 8^n.

a(n) = (8^(n+1) - 64)/7.

a(n) = 9*a(n-1) - 8*a(n-2).

a(n) = A052379(n) - 8. - Michel Marcus, Sep 25 2014