A055428 Number of points in Z^n of norm <= 4.

1, 9, 49, 257, 1281, 5913, 23793, 88273, 306049, 995241, 3083569, 9217057, 26631041, 74164665, 198807793, 513829617, 1284656385, 3117323593, 7360510001, 16939394369, 38039783425, 83427144281, 178841051889

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Crossrefs

Row n=4 of A302997.

Programs

Mathematica

a[n_] := SeriesCoefficient[1/(1-x) Sum[x^(i^2), {i, -4, 4}]^n, {x, 0, 16}];
a /@ Range[0, 22] (* Jean-François Alcover, Sep 29 2019, from A302997 *)

Formula

Empirical g.f.: -(1201*x^16 +46896*x^15 +180864*x^14 -238504*x^13 -86788*x^12 +380032*x^11 -353440*x^10 +186568*x^9 -65418*x^8 +17264*x^7 -3968*x^6 +1000*x^5 -164*x^4 -32*x^3 +32*x^2 -8*x +1) / (x -1)^17. - Colin Barker, Jul 07 2013

Above conjecture confirmed by later additions of b-file from Andrew Howroyd and program from Jean-François Alcover with connection to A302997. - Ray Chandler, Jun 27 2024