A247840 a(n) = Sum_{k=2..n} 6^k.

0, 36, 252, 1548, 9324, 55980, 335916, 2015532, 12093228, 72559404, 435356460, 2612138796, 15672832812, 94036996908, 564221981484, 3385331888940, 20311991333676, 121871948002092, 731231688012588, 4387390128075564, 26324340768453420

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 (7,-6).

Crossrefs

Cf. similar sequences listed in A247817.

Cf. A000400, A003464, A105281.

Programs

Magma

[0] cat [&+[6^k: k in [2..n]]: n in [2..30]];

Magma

[(6^(n+1)-36)/5: n in [1..30]];

Mathematica

RecurrenceTable[{a[1] == 0, a[n] == a[n-1] + 6^n}, a, {n, 30}] (* or *) CoefficientList[Series[36 x / ((1 - x) (1 - 6 x)), {x, 0, 30}], x]
Join[{0},Accumulate[6^Range[2,30]]] (* or *) LinearRecurrence[{7,-6},{0,36},30] (* Harvey P. Dale, Jun 11 2016 *)

PARI

a(n) = sum(k=2, n, 6^k); \\ Michel Marcus, Sep 25 2014

Formula

G.f.: 36*x^2/((1-x)*(1-6*x)).

a(n) = a(n-1) + 6^n = (6^(n+1) - 36)/5 = 7*a(n-1) - 6*a(n-2).

a(n) = A105281(n) - 6. - Michel Marcus, Sep 25 2014

a(n) = 36 * A003464(n-1). - Alois P. Heinz, Jan 14 2025