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
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).
Programs
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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) ;
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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 *) -
PARI
Vec(-x*(-1-x+x^2) / ( (1+x)^3*(x-1)^4 ) + O(x^80)) \\ Michel Marcus, Apr 01 2015
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
Extensions
Edited by Omar E. Pol, Feb 08 2010
Comments