|
%I #17 Jun 21 2021 16:32:20
%S 1,3,13,56,241,1037,4462,19199,82609,355448,1529413,6580721,28315366,
%T 121834667,524227237,2255632184,9705479209,41760499493,179686059838,
%U 773148800711,3326685824041,14313982718072,61589856118237,265007332436969,1140267093830134
%N Expansion of (1-x)^2/(1-5*x+3*x^2).
%C a(n) is the number of generalized compositions of n when there are i+2 different types of i, (i=1,2,...). [_Milan Janjic_, Sep 24 2010]
%H P. J. Cameron, <a href="http://dx.doi.org/10.1016/0012-365X(89)90081-2">Some sequences of integers</a>, Discrete Math., 75 (1989), 89-102.
%H P. J. Cameron, <a href="http://dx.doi.org/10.1016/S0167-5060(08)70569-7">Some sequences of integers</a>, in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3).
%F a(n+2) = 5a(n+1) - 3a(n) (n >= 1); a(0) = 1, a(1) = 3, a(2) = 13.
%t CoefficientList[Series[(1-x)^2/(1-5x+3x^2),{x,0,30}],x] (* or *) LinearRecurrence[{5,-3},{1,3,13},30] (* _Harvey P. Dale_, Jun 21 2021 *)
%o (PARI) a(n)=polcoeff((1-x)^2/(1-5*x+3*x^2)+x*O(x^n),n)
%Y Cf. A003480, A010903, A010920; equals A095939 + A095940.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 13 2004
|
