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A033116
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Base-6 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, 6, 37, 222, 1333, 7998, 47989, 287934, 1727605, 10365630, 62193781, 373162686, 2238976117, 13433856702, 80603140213, 483618841278, 2901713047669, 17410278286014, 104461669716085, 626770018296510, 3760620109779061
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Partial sums of A015540. [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 (6,1,-6).
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FORMULA
| G.f.: x / ( (1-x)*(1-6*x)*(1+x) ). a(n) = 6^(n+1)/35 -1/10 -(-1)^n/14. - R. J. Mathar, Jan 08 2011
a(n)=floor(6^(n+1)/35). a(n+1)=sum{k=0..floor(n/2)} 6^(n-2*k). a(n+1)=sum{k=0..n} sum{j=0..k} (-1)^(j+k)*6^j. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003, index corrected R. J. Mathar, Jan 08 2011
a(n) = 5*a(n-1) +6*a(n-2)+1. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2008]
a(n) = floor(6^(n+1)/7)/5 = floor((6*6^n-1)/35) = round((12*6^n-7)/70) = round((6*6^n-6)/35) = ceil((6*6^n-6)/35). a(n)=a(n-2)+6^(n-1), n>2. [From Mircea Merca (mircea(AT)teacher.com), Dec 28 2010]
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=5*a[n-1]+6*a[n-2]+1 od: seq(a[n], n=1..33); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2008]
A033116 := proc(n) 6^(n+1)/35 -1/10 -(-1)^n/14 ; end proc: # R. J. Mathar, Jan 08 2011
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MATHEMATICA
| Join[{a=1, b=6}, Table[c=5*b+6*a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 06 2011*)
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PROG
| (MAGMA) [Round((12*6^n-7)/70): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011
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CROSSREFS
| Cf. A015540
Sequence in context: A057418 A001419 A081152 * A033124 A180032 A022035
Adjacent sequences: A033113 A033114 A033115 * A033117 A033118 A033119
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KEYWORD
| nonn,easy,base
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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