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A000472 a(n) = a(n-1)^2 + (a(n-2) + 1)*(a(n-1) - a(n-2)^2). 1

%I #28 Sep 08 2022 08:44:28

%S 2,5,28,802,643726,414383582242,171713753231982206218246,

%T 29485613049014079571725771288849499850026859242

%N a(n) = a(n-1)^2 + (a(n-2) + 1)*(a(n-1) - a(n-2)^2).

%D Damiani, E.; D'Antona, O.; Naldi, G.; and Pavarino, L.; Tiling bricks with bricks. Stud. Appl. Math. 83 (1990), number 2, 91-110.

%H Vincenzo Librandi, <a href="/A000472/b000472.txt">Table of n, a(n) for n = 1..14</a>

%H <a href="/index/Br#bricks">Index entries for sequences related to bricks</a>

%p A000472 := proc(n) option remember; if n<=2 then 3*n-1 else A000472(n-1)^2+(1+A000472(n-2))*(A000472(n-1)-A000472(n-2)^2); fi; end;

%t RecurrenceTable[{a[1]==2,a[2]==5,a[n]==a[n-1]^2+(a[n-2]+1)(a[n-1]- a[n-2]^2)}, a[n],{n,10}] (* _Harvey P. Dale_, Sep 29 2011 *)

%o (Magma) I:=[2,5]; [n le 2 select I[n] else Self(n-1)^2 + (Self(n-2)+1)*(Self(n-1)-Self(n-2)^2 ): n in [1..10]]; // _Vincenzo Librandi_, Sep 30 2011

%o (Haskell)

%o a000472 n = a000472_list !! (n-1)

%o a000472_list = 2 : 5 : zipWith (+) (map (^ 2) $ tail a000472_list)

%o (zipWith (*) (map (+ 1) a000472_list)

%o (zipWith (-) (tail a000472_list)

%o (map (^ 2) a000472_list)))

%o -- _Reinhard Zumkeller_, Oct 03 2012

%K nonn,nice,easy

%O 1,1

%A Ottavio D'Antona [ dantona(AT)hermes.dsi.unimi.it ]

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)