OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-5).
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
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 *)
PROG
(PARI) a(n) = sum(m=0, n, 6*5^m); \\ Michel Marcus, Nov 03 2017
(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
(SageMath) [3*(5^(n+1) -1)/2 for n in range(41)] # G. C. Greubel, Oct 12 2022
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Nov 02 2008
STATUS
approved