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A033115 Base-5 digits are, in order, the first n terms of the periodic sequence with initial period 1,0. 5
1, 5, 26, 130, 651, 3255, 16276, 81380, 406901, 2034505, 10172526, 50862630, 254313151, 1271565755, 6357828776, 31789143880, 158945719401, 794728597005, 3973642985026, 19868214925130, 99341074625651, 496705373128255 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of A015531. [From 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

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 }}. - Paul Barry, Nov 12 2003

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. - Paul Barry, Nov 12 2003

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)=ceil((5*5^n-5)/24); a(n)=a(n-2)+5^(n-1),n>1. [From Mircea Merca, Dec 28 2010]

MAPLE

seq(1/3*floor(5^(n+1)/8), n=1..32); [From Mircea Merca, Dec 26 2010]

MATHEMATICA

Join[{a=1, b=5}, Table[c=4*b+5*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)

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: A247491 A244617 A003583 * A033123 A047770 A047757

Adjacent sequences:  A033112 A033113 A033114 * A033116 A033117 A033118

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified June 28 20:39 EDT 2017. Contains 288840 sequences.