A016150 Expansion of g.f. 1/((1-4*x)*(1-7*x)).

1, 11, 93, 715, 5261, 37851, 269053, 1899755, 13363821, 93808891, 657710813, 4608169995, 32273967181, 225984879131, 1582162589373, 11076211867435, 77537778039341, 542781626144571, 3799540102488733, 26597055595328075, 186180488678924301, 1303267818798981211, 9122892323778912893

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (11,-28).

Crossrefs

Cf. A190542.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)))); // Vincenzo Librandi, Jun 24 2013

Mathematica

Join[{a=1,b=11},Table[c=11*b-28*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2011 *)
CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 24 2013 *)
LinearRecurrence[{11,-28},{1,11},20] (* Harvey P. Dale, Mar 11 2020 *)

PARI

Vec(1/((1-4*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

[lucas_number1(n,11,28) for n in range(1, 20)] # Zerinvary Lajos, Apr 27 2009

Formula

From Barry E. Williams, Jan 13 2000: (Start)

a(n) = (7^(n+1) - 4^(n+1))/3.

a(n) = 11*a(n-1) - 28*a(n-2) for n>0, a(0)=1. (End)

a(n) = Sum_{k=0..n} 7^k*4^(n-k). - Bruno Berselli, Aug 07 2013

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(4*x)*(7*exp(3*x) - 4)/3.

a(n) = A190542(n+1)/3. (End)