OFFSET
0,1
REFERENCES
Encyclopaedia Britannica, 1965 ed., Vol. 16 pp. 755-756.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = a(n-1) + 6*n - 10 (with a(0)=6). - Vincenzo Librandi, Nov 19 2010
From Colin Barker, May 22 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 2*(3 - 8*x + 8*x^2)/(1 - x)^3. (End)
E.g.f.: (6 - 4*x + 3*x^2)*exp(x). - G. C. Greubel, Aug 24 2022
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {6, 2, 4}, 61] (* G. C. Greubel, Aug 24 2022 *)
PROG
(PARI) a(n)=3*n^2-7*n+6 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [((6*n-7)^2+23)/12: n in [0..60]]; // G. C. Greubel, Aug 24 2022
(SageMath) [3*n^2-7*n+6 for n in (0..60)] # G. C. Greubel, Aug 24 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved