A016304 Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)).
1, 15, 157, 1419, 11869, 94731, 733069, 5551323, 41378557, 304766187, 2224062061, 16112628987, 116053574365, 831966057483, 5941308640333, 42294437942811, 300292730428093, 2127439102098219, 15044413649559085
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (15,-68,84).
Programs
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Magma
[ n eq 1 select 1 else n eq 2 select 15 else n eq 3 select 157 else 15*Self(n-1)-68*Self(n-2) +84*Self(n-3): n in [1..20] ]; // Vincenzo Librandi, Aug 25 2011
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Mathematica
CoefficientList[Series[1/((1-2x)(1-6x)(1-7x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -68, 84}, {1, 15, 157}, 30] -
PARI
Vec(1/((1-2*x)*(1-6*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
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Sage
[(7^n - 2^n)/5-(6^n - 2^n)/4 for n in range(2,21)] # Zerinvary Lajos, Jun 05 2009
Formula
a(n) = (7^(n+2) - 2^(n+2))/5-(6^(n+2) - 2^(n+2))/4. - Zerinvary Lajos, Jun 05 2009 [corrected by Joerg Arndt, Aug 25 2011]
From Vincenzo Librandi, Aug 25 2011: (Start)
a(n) = 15*a(n-1) - 68*a(n-2) + 84*a(n-3) for n > 2;
a(n) = 13*a(n-1) - 42*a(n-2) + 2^n for n > 1. (End)
E.g.f.: exp(2*x)*(1 - 45*exp(4*x) + 49*exp(5*x))/5. - Stefano Spezia, Aug 25 2025