A146883 a(n) = 6 * Sum_{m=0..n} 5^m.

6, 36, 186, 936, 4686, 23436, 117186, 585936, 2929686, 14648436, 73242186, 366210936, 1831054686, 9155273436, 45776367186, 228881835936, 1144409179686, 5722045898436, 28610229492186, 143051147460936, 715255737304686

Offset: 0

Author

Roger L. Bagula, Nov 02 2008

Keywords

• nonn
• easy
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A003463, A100774.

Programs

Magma

[n le 2 select 6^n else 6*Self(n-1) -5*Self(n-2): n in [1..31]]; // G. C. Greubel, Oct 12 2022

Mathematica

a[n_]:= 6*Sum[5^m, {m,0,n}]; Table[a[n], {n,0,30}]
(* Second programs: *)
Array[3(5^(#+1) -1)/2 &, 21, 0] (* or *)
CoefficientList[Series[6/((1-x)(1-5x)), {x, 0, 20}], x] (* Michael De Vlieger, Nov 02 2017 *)
LinearRecurrence[{6,-5},{6,36},30] (* Harvey P. Dale, Jan 07 2024 *)

PARI

a(n) = sum(m=0, n, 6*5^m); \\ Michel Marcus, Nov 03 2017

SageMath

[3*(5^(n+1) -1)/2 for n in range(41)] # G. C. Greubel, Oct 12 2022

Formula

a(n) = Sum_{m=0..n} 6*5^m.

a(n) = 3*(5^(n+1) - 1)/2. - Emeric Deutsch, Nov 02 2017

G.f.: 6/((1-z)*(1-5*z)). - Robert Israel, Nov 02 2017

a(n) = 6 * A003463(n+1). - Alois P. Heinz, Nov 03 2017

E.g.f.: (3/2)*(5*exp(5*x) - exp(x)). - G. C. Greubel, Oct 12 2022