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A154533 Number of constants of the form a^3*u + b*c*v, where a, b, c are linear, u of order n-3 and v of order n-2.

%I A154533 #31 Sep 08 2022 08:45:40
%S A154533 10,9,10,13,18,25,34,45,58,73,90,109,130,153,178,205,234,265,298,333,
%T A154533 370,409,450,493,538,585,634,685,738,793,850,909,970,1033,1098,1165,
%U A154533 1234,1305,1378,1453,1530,1609,1690,1773,1858,1945,2034,2125,2218,2313
%N A154533 Number of constants of the form a^3*u + b*c*v, where a, b, c are linear, u of order n-3 and v of order n-2.
%H A154533 Emanuel Lasker, <a href="https://gdz.sub.uni-goettingen.de/en/dms/loader/img/?PID=GDZPPN002259613">Zur Theorie der kanonischen Formen</a>, Mathematische Annalen, 58 (1904), 434-440.
%H A154533 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A154533 a(n) = n^2 - 2*n + 10.
%F A154533 a(n) = a(n-1) + 2*n-3 (with a(0)=10). - _Vincenzo Librandi_, Nov 27 2010
%F A154533 G.f.: (-10 + 21*x - 13*x^2) / (x-1)^3 . - _R. J. Mathar_, Aug 31 2011
%t A154533 LinearRecurrence[{3,-3,1},{10,9,10},60] (* _Harvey P. Dale_, May 04 2016 *)
%o A154533 (Sage) [lucas_number1(3,n,-9) for n in range(-1, 49)] # _Zerinvary Lajos_, May 16 2009
%o A154533 (Magma) [ n^2-2*n+10: n in [0..50] ];
%o A154533 (PARI) a(n)=n^2-2*n+10 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A154533 Cf. A189834.
%K A154533 nonn,easy
%O A154533 0,1
%A A154533 _Reinhard Zumkeller_, Jan 11 2009