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Series expansion for rectilinear polymers on square lattice.
(Formerly M4440)
0

%I M4440 #16 Oct 21 2022 21:26:44

%S 7,63,254,710,1605,3157,5628,9324,14595,21835,31482,44018,59969,79905,

%T 104440,134232,169983,212439,262390,320670,388157,465773,554484,

%U 655300,769275,897507,1041138,1201354,1379385

%N Series expansion for rectilinear polymers on square lattice.

%D V. B. Priezzhev, Series expansion for rectilinear polymers on the square lattice, J. Phys. A 12 (1979), 2131-2139.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).

%F G.f.: (7 + 28x + 9 x^2 ) / ( 1 - x )^5.

%F a(n)=n(n-1)(11n^2-13n+3)/6 - _T. D. Noe_, Feb 09 2007

%F a(2)=7, a(3)=63, a(4)=254, a(5)=710, a(6)=1605, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - _Harvey P. Dale_, Oct 17 2012

%t Table[(n(n-1)(11n^2-13n+3))/6,{n,2,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{7,63,254,710,1605},40] (* _Harvey P. Dale_, Oct 17 2012 *)

%o (PARI) a(n)=n*(n-1)*(11*n^2-13*n+3)/6 \\ _Charles R Greathouse IV_, Oct 21 2022

%K nonn,easy

%O 2,1

%A _Simon Plouffe_