A228219 -id:A228219 - cp's OEIS frontend

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

Vincenzo Librandi, Apr 20 2016

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?

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).

Cf. A000292, A000330, A000578, A002411, A004068, A005900, A006003, A167875, A168668, A228219, A272124, A272130.

Magma
```
[10*n^2+4*n+1: n in [0..50]];
```

Table[10 n^2 + 4 n + 1, {n, 0, 50}]
LinearRecurrence[{3,-3,1},{1,15,49},50] (* Harvey P. Dale, Dec 26 2021 *)

a(n)=10*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017

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.

Edited by Bruno Berselli, Apr 22 2016

cp's OEIS Frontend

A272039 a(n) = 10n^2 + 4n + 1.

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