A016135 Expansion of g.f. 1/((1-2*x)*(1-11*x)).
1, 13, 147, 1625, 17891, 196833, 2165227, 23817625, 261994131, 2881935953, 31701296507, 348714263625, 3835856903971, 42194425951873, 464138685486987, 5105525540389625, 56160780944351411, 617768590387996593, 6795454494268224667, 74749999436950995625, 822249993806462000451
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (13,-22).
Crossrefs
Cf. A139740.
Programs
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Mathematica
LinearRecurrence[{13,-22},{1,13},30] (* or *) CoefficientList[Series[ 1/((1-2x)*(1-11x)),{x,0,30}],x] (* Harvey P. Dale, Oct 15 2011 *) -
PARI
a(n)=(11^n++-2^n)/9 \\ Charles R Greathouse IV, Mar 26 2012
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Sage
[(11^(n+1) - 2^(n+1))/9 for n in range(0,20)] # Zerinvary Lajos, Jun 05 2009
Formula
a(n) = (11^(n+1) - 2^(n+1))/9. - Zerinvary Lajos, Jun 05 2009
a(n) = 13*a(n-1) - 22*a(n-2). - Vincenzo Librandi, Jun 02 2011
From Elmo R. Oliveira, Mar 08 2025: (Start)
E.g.f.: exp(2*x)*(11*exp(9*x) - 2)/9.
a(n) = A139740(n+1)/9. (End)
Extensions
Incorrect comment removed by Charles R Greathouse IV, Mar 26 2012