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

0,1

Links

Table of n, a(n) for n=0..49.

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).

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

Mathematica

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

Prog

(Sage) [lucas_number1(3, n, -9) for n in range(-1, 49)] # Zerinvary Lajos, May 16 2009
(Magma) [ n^2-2*n+10: n in [0..50] ];
(PARI) a(n)=n^2-2*n+10 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A189834.

Sequence in context: A070641 A231471 A063661 * A167608 A063596 A360382

Adjacent sequences: A154530 A154531 A154532 * A154534 A154535 A154536

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 11 2009

Status

approved