OFFSET
0,2
COMMENTS
Polynomials from the table "Coefficients and roots of Ehrhart polynomials" in Beck et al. paper (see Links section):
. Cube: A000578;
. Cube minus corner: A004068;
. Prism: A002411;
. Octahedron: A005900;
. Square pyramid: A000330;
. Bypyramid: A006003;
. Unimodular tetrahedron: A000292;
. Fat tetrahedron: A167875;
. Cyclic(2,5), which has the same polynomial form of this sequence.
a(n) for n = 0, -1, 1, -2, 2, -3, 3, ... gives all x such that (5*x - 3)/2 is a square.
Squares in sequence: 1, 49, 1385329, 101263969, 2880599856289, ...
Is this 1 followed by A228219?
LINKS
M. Beck, J. A. De Loera, M. Develin, J. Pfeifle and R. P. Stanley, Coefficients and roots of Ehrhart Polynomials, page 19.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
O.g.f.: (1 + 12*x + 7*x^2)/(1 - x)^3.
E.g.f.: (1 + 14*x + 10*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = 2*A168668(n) + 1.
MATHEMATICA
Table[10 n^2 + 4 n + 1, {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {1, 15, 49}, 50] (* Harvey P. Dale, Dec 26 2021 *)
PROG
(Magma) [10*n^2+4*n+1: n in [0..50]];
(PARI) a(n)=10*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 20 2016
EXTENSIONS
Edited by Bruno Berselli, Apr 22 2016
STATUS
approved