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A014827
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a(1)=1, a(n)=5*a(n-1)+n.
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8
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1, 7, 38, 194, 975, 4881, 24412, 122068, 610349, 3051755, 15258786, 76293942, 381469723, 1907348629, 9536743160, 47683715816, 238418579097, 1192092895503, 5960464477534, 29802322387690, 149011611938471
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 (7,-11,5).
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FORMULA
| a(n) = (5^(n+1)-4*n-5)/16.
G.f.: x/((1-5*x)*(1-x)^2).
a(n) = sum{k=0..n, (n-k)*5^k}=sum{k=0..n, k*5^(n-k)} - Paul Barry, Jul 30 2004
a(n) = sum{k=0..n, binomial(n+2, k+2)*4^k} [Offset 0] - Paul Barry, Jul 30 2004
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MAPLE
| a:=n->sum((5^(n-j)-1^(n-j))/4, j=0..n): seq(a(n), n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007
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MATHEMATICA
| Join[{a=1, b=7}, Table[c=6*b-5*a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 06 2011*)
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PROG
| (Sage) [(gaussian_binomial(n, 1, 5)-n)/4 for n in xrange(2, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
(MAGMA) [(5^(n+1)-4*n-5)/16: n in [1..30]]; // Vincenzo Librandi, Aug 23 2011
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CROSSREFS
| Cf. A016218, A016208, A000392, A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A016256.
Sequence in context: A037605 A128726 A055146 * A141845 A048437 A099461
Adjacent sequences: A014824 A014825 A014826 * A014828 A014829 A014830
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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