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

0,2

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).

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

Mathematica

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

Crossrefs

Row n=2 of A302997.

Sequence in context: A027051 A109786 A283959 * A146621 A147086 A032406

Adjacent sequences: A055423 A055424 A055425 * A055427 A055428 A055429

Keyword

nonn,easy

Author

David W. Wilson

Status

approved