A005062 a(n) = 6^n - 5^n.
0, 1, 11, 91, 671, 4651, 31031, 201811, 1288991, 8124571, 50700551, 313968931, 1932641711, 11839990891, 72260648471, 439667406451, 2668522016831, 16163719991611, 97745259402791, 590286253682371
Offset: 0
Examples
G.f. = x + 11*x^2 + 91*x^3 + 671*x^4 + 4651*x^5 + 31031*x^6 + 201811*x^7 + ... - _Michael Somos_, Jul 14 2018
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (11,-30).
Programs
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Magma
[6^n - 5^n: n in [0..25]]; // Vincenzo Librandi, Jun 03 2011
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Maple
restart:a:=n->sum(5^(n-j)*binomial(n,j),j=1..n): seq(a(n), n=0..19); # Zerinvary Lajos, Apr 18 2009
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Mathematica
f[n_]:=6^n-5^n;f[Range[0,60]] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2011 *) LinearRecurrence[{11,-30},{0,1},20] (* Harvey P. Dale, May 28 2015 *)
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PARI
a(n)=6^n-5^n \\ M. F. Hasler, May 03 2015
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PARI
for(d=0,9,print1(sum(n=1,10^d-1,vecmax(digits(n))==5)",")) \\ Only to illustrate the comment about "largest digit equals 5".
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Sage
[lucas_number1(n,11,30) for n in range(0, 20)] # Zerinvary Lajos, Apr 27 2009
Formula
G.f.: x/((1-5*x)(1-6*x)).
a(n) = 11*a(n-1) - 30*a(n-2), n > 1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009
E.g.f.: exp(6*x) - exp(5*x). - Mohammad K. Azarian, Jan 14 2009
a(n) = -(30)^n * a(-n) for all n in Z. - Michael Somos, Jul 14 2018
Comments