A275876 a(n) = 4*n*(n^2 - 3*n - 1)/3.

0, -4, -8, -4, 16, 60, 136, 252, 416, 636, 920, 1276, 1712, 2236, 2856, 3580, 4416, 5372, 6456, 7676, 9040, 10556, 12232, 14076, 16096, 18300, 20696, 23292, 26096, 29116, 32360, 35836, 39552, 43516, 47736, 52220, 56976, 62012, 67336, 72956, 78880, 85116, 91672, 98556, 105776, 113340, 121256

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Peter John Hilton and Jean Pedersen, Descartes, Euler, Poincaré, Pólya and Polyhedra, L'Enseign. Math., 27 (1981), 327-343. See Cor. 2.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From Colin Barker, Aug 15 2016: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.

G.f.: -4*x*(1-2*x-x^2) / (1-x)^4. (End)

E.g.f.: 4*x*(-3 + x^2)*exp(x)/3. - G. C. Greubel, Apr 28 2019

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {0, -4, -8, -4}, 50] (* G. C. Greubel, Apr 28 2019 *)

Prog

(PARI) concat(0, Vec(-4*x*(1-2*x-x^2)/(1-x)^4 + O(x^50))) \\ Colin Barker, Aug 15 2016
(Magma) [4*n*(n^2-3*n-1)/3: n in [0..50]]; // G. C. Greubel, Apr 28 2019
(Sage) [4*n*(n^2-3*n-1)/3 for n in (0..50)] # G. C. Greubel, Apr 28 2019
(GAP) List([0..50], n-> 4*n*(n^2-3*n-1)/3) # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A019254 A304293 A055374 * A255293 A019246 A019192

Adjacent sequences: A275873 A275874 A275875 * A275877 A275878 A275879

Keyword

sign,easy

Author

N. J. A. Sloane, Aug 14 2016

Status

approved