A027599 a(n) = 3*n^2 - 7*n + 6.

6, 2, 4, 12, 26, 46, 72, 104, 142, 186, 236, 292, 354, 422, 496, 576, 662, 754, 852, 956, 1066, 1182, 1304, 1432, 1566, 1706, 1852, 2004, 2162, 2326, 2496, 2672, 2854, 3042, 3236, 3436, 3642, 3854, 4072, 4296, 4526, 4762, 5004, 5252, 5506

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

Cf. A049450.

Sequence in context: A169843 A329591 A123139 * A351297 A248272 A058160

Adjacent sequences: A027596 A027597 A027598 * A027600 A027601 A027602

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved