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A272039
a(n) = 10*n^2 + 4*n + 1.
4
1, 15, 49, 103, 177, 271, 385, 519, 673, 847, 1041, 1255, 1489, 1743, 2017, 2311, 2625, 2959, 3313, 3687, 4081, 4495, 4929, 5383, 5857, 6351, 6865, 7399, 7953, 8527, 9121, 9735, 10369, 11023, 11697, 12391, 13105, 13839, 14593, 15367, 16161, 16975, 17809, 18663, 19537
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.
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 20 2016
EXTENSIONS
Edited by Bruno Berselli, Apr 22 2016
STATUS
approved