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A033115
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Base-5 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.
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5
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Partial sums of A015531. [From Mircea Merca, Dec 28 2010]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (5,1,-5).
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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 (pbarry(AT)wit.ie), 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 (pbarry(AT)wit.ie), 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]
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MAPLE
| seq(1/3*floor(5^(n+1)/8), n=1..32); [From Mircea Merca, Dec 26 2010]
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MATHEMATICA
| Join[{a=1, b=5}, Table[c=4*b+5*a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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PROG
| (MAGMA) [Round((5*5^n-3)/24): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011
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CROSSREFS
| Cf. A015531.
Sequence in context: A185552 A171702 A003583 * A033123 A047770 A047757
Adjacent sequences: A033112 A033113 A033114 * A033116 A033117 A033118
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KEYWORD
| nonn,base,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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