A160790 Vertex number of a rectangular spiral. The first differences (A160791) are the edge lengths of the spiral. The distances between two nearest edges, that are parallel to the initial edge, are the natural numbers.

0, 1, 2, 4, 7, 10, 16, 20, 30, 35, 50, 56, 77, 84, 112, 120, 156, 165, 210, 220, 275, 286, 352, 364, 442, 455, 546, 560, 665, 680, 800, 816, 952, 969, 1122, 1140, 1311, 1330, 1520, 1540, 1750, 1771, 2002, 2024, 2277, 2300, 2576, 2600, 2900, 2925, 3250, 3276, 3627, 3654, 4032, 4060, 4466, 4495, 4930, 4960, 5425

Offset

0,3

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

a(n) = +a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7).

G.f.: -x*(-1-x+x^2) / ( (1+x)^3*(x-1)^4 ).

a(n) = (2*n+3+(-1)^n)*(2*n+3-3*(-1)^n)*(2*n+15+5*(-1)^n)/384. - Luce ETIENNE, Mar 31 2015

Maple

A160791 := proc(n) if type(n, 'odd') then ceil(n/2) ; else A000217(n/2) ; end if; end proc:
A160790 := proc(n) if n = 0 then 0; else add(A160791(i), i=0..n) ; end if; end proc:
seq(A160790(n), n=0..60) ;

Mathematica

Table[(2*n + 3 + (-1)^n)*(2*n + 3 - 3*(-1)^n)*(2*n + 15 + 5*(-1)^n)/ 384, {n, 0, 60}] (* Michael De Vlieger, Mar 31 2015 *)

Prog

(PARI) Vec(-x*(-1-x+x^2) / ( (1+x)^3*(x-1)^4 ) + O(x^80)) \\ Michel Marcus, Apr 01 2015

Crossrefs

Cf. A160791, A160792.

Sequence in context: A226136 A364612 A176099 * A173726 A000376 A000375

Adjacent sequences: A160787 A160788 A160789 * A160791 A160792 A160793

Keyword

easy,nonn

Author

Omar E. Pol, May 29 2009

Extensions

Edited by Omar E. Pol, Feb 08 2010

Status

approved