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A016127
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Expansion of 1/((1-2*x)*(1-5*x)).
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11
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1, 7, 39, 203, 1031, 5187, 25999, 130123, 650871, 3254867, 16275359, 81378843, 406898311, 2034499747, 10172515119, 50862608363, 254313107351, 1271565667827, 6357828601279, 31789143530683
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| With leading zero, binomial transform of A002450. - Paul Barry (pbarry(AT)wit.ie), Apr 11 2003
The sequence of fractions a(n)/(n+1) is the 3rd binomial transform of the sequence of fractions J(n+1)/(n+1) where J(n) is A001045(n). - Paul Barry (pbarry(AT)wit.ie), Aug 05 2005
Equals term (1,2) in M^n, M = the 3x3 matrix [1, 1, 3; 1, 3, 1; 3, 1, 1]. a(n)/ a(n-1) tends to 5, a root to the charpoly x^3 - 5x^2 -4x + 20. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 12 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index to sequences with linear recurrences with constant coefficients, signature (7,-10).
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FORMULA
| a(n) =(5^(n+1)-2^(n+1))/3 = sum(0<=i<=n, 5^i*2^(n-1) ) = 5*a(n-1)+2^n =2*a(n-1)+5^n. - Henry Bottomley (se16(AT)btinternet.com), Apr 07 2003
Binomial transform of A020989. - Paul Barry (pbarry(AT)wit.ie), May 18 2003
a(n) = sum(k=0..n, sum(j=0..n, 5^(n-j)*binomial(j, k) ) ); a(n)=sum(k=0..n, 2^k*5^(n-k) ) = sum(k=0..n, 5^k*2^(n-k) ); - Paul Barry (pbarry(AT)wit.ie), Aug 05 2005
For n>2, a(n) = 9*a(n-1) - 24*a(n-2) + 20*a(n-3). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 26 2007
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MATHEMATICA
| Join[{a=1, b=7}, Table[c=7*b-10*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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PROG
| (Sage) [lucas_number1(n, 7, 10) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
(Sage) [(5^n - 2^n)/3 for n in xrange(1, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
(MAGMA) [(5^(n+1)-2^(n+1))/3: n in [0..30]]; /7 Vincenzo Librandi, Jun 08 2011
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CROSSREFS
| Sequence in context: A026752 A026379 A026708 * A099460 A092923 A164550
Adjacent sequences: A016124 A016125 A016126 * A016128 A016129 A016130
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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