A055426 Number of points in Z^n of norm <= 2.

1, 5, 13, 33, 89, 221, 485, 953, 1713, 2869, 4541, 6865, 9993, 14093, 19349, 25961, 34145, 44133, 56173, 70529, 87481, 107325, 130373, 156953, 187409, 222101, 261405, 305713, 355433, 410989, 472821, 541385, 617153, 700613, 792269, 892641

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Row n=2 of A302997. Column 4 of A122510.

Programs

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{1,5,13,33,89},40] (* Harvey P. Dale, Feb 09 2015 *)

Formula

a(n) = (3+2*n+16*n^2-8*n^3+2*n^4)/3. - corrected by Colin Barker, Jul 07 2013

G.f.: -(x+1)*(9*x^3-x^2-x+1) / (x-1)^5. - Colin Barker, Jul 07 2013

a(0)=1, a(1)=5, a(2)=13, a(3)=33, a(4)=89, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Feb 09 2015