A028164 - OEIS

%I #24 Aug 06 2024 02:42:48

%S 1,37,875,16865,288891,4584297,68969155,997819105,14012533931,

%T 192242650457,2588592449235,34328260342545,449522440061371,

%U 5824352378123017,74789809096438115,953017761256677185

%N Expansion of 1/((1-4x)(1-10x)(1-11x)(1-12x)).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (37,-494,2768,-5280).

%F From _Vincenzo Librandi_, Mar 16 2011: (Start)

%F a(n) = 23*a(n-1) - 132*a(n-2) + (10^(n+1) - 4^(n+1))/6, n >= 2.

%F a(n) = 37*a(n-1) - 494*a(n-2) + 2768*a(n-3) - 5280*a(n-4), n >= 4. (End)

%F a(n) = -2^(2*n+2)/21 - 11^(n+3)/7 + 25*10^(n+1)/3 + 9*12^(n+1). - _R. J. Mathar_, Mar 18 2011

%t CoefficientList[Series[1/((1-4x)(1-10x)(1-11x)(1-12x)),{x,0,20}],x] (* or *) LinearRecurrence[{37,-494,2768,-5280},{1,37,875,16865},20] (* _Harvey P. Dale_, Dec 20 2023 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_