OFFSET
1,2
COMMENTS
Partial sums of A015531. - Mircea Merca, Dec 28 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,1,-5).
FORMULA
a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3). - Joerg Arndt, Jan 08 2011
From Paul Barry, Nov 12 2003: (Start)
a(n) = floor(5^(n+2)/24);
a(n) = Sum_{k=0..floor(n/2)} 5^(n-2*k);
a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(j+k)*5^j.
Partial sums of A083425.
G.f.: 1/((1-x)*(1+x)*(1-5*x));
a(n) = 4*a(n-1) + 5*a(n-2) + 1. (End)
From Mircea Merca, Dec 28 2010: (Start)
a(n) = (1/3)*floor(5^(n+1)/8) = floor((5*5^n - 1)/24) = round((5*5^n - 3)/24) = round((5*5^n - 5)/24) = ceiling((5*5^n - 5)/24);
a(n) = a(n-2) + 5^(n-1), n > 1. (End)
MAPLE
seq(1/3*floor(5^(n+1)/8), n=1..32); # Mircea Merca, Dec 26 2010
MATHEMATICA
Table[FromDigits[PadRight[{}, n, {1, 0}], 5], {n, 30}] (* or *) LinearRecurrence[ {5, 1, -5}, {1, 5, 26}, 30] (* Harvey P. Dale, Jan 28 2017 *)
PROG
(Magma) [Round((5*5^n-3)/24): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved