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.

10, 9, 10, 13, 18, 25, 34, 45, 58, 73, 90, 109, 130, 153, 178, 205, 234, 265, 298, 333, 370, 409, 450, 493, 538, 585, 634, 685, 738, 793, 850, 909, 970, 1033, 1098, 1165, 1234, 1305, 1378, 1453, 1530, 1609, 1690, 1773, 1858, 1945, 2034, 2125, 2218, 2313

Offset: 0

Author

Reinhard Zumkeller, Jan 11 2009

Keywords

• nonn
• easy

Links

• Emanuel Lasker, Zur Theorie der kanonischen Formen, Mathematische Annalen, 58 (1904), 434-440.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A189834.

Programs

Magma

[ n^2-2*n+10: n in [0..50] ];

Mathematica

LinearRecurrence[{3,-3,1},{10,9,10},60] (* Harvey P. Dale, May 04 2016 *)

PARI

a(n)=n^2-2*n+10 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[lucas_number1(3,n,-9) for n in range(-1, 49)] # Zerinvary Lajos, May 16 2009

Formula

a(n) = n^2 - 2*n + 10.

a(n) = a(n-1) + 2*n-3 (with a(0)=10). - Vincenzo Librandi, Nov 27 2010

G.f.: (-10 + 21*x - 13*x^2) / (x-1)^3 . - R. J. Mathar, Aug 31 2011