A033115 Base-5 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.

1, 5, 26, 130, 651, 3255, 16276, 81380, 406901, 2034505, 10172526, 50862630, 254313151, 1271565755, 6357828776, 31789143880, 158945719401, 794728597005, 3973642985026, 19868214925130, 99341074625651, 496705373128255

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

Cf. A015531.

Sequence in context: A339892 A244617 A003583 * A033123 A331883 A047770

Adjacent sequences: A033112 A033113 A033114 * A033116 A033117 A033118

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved