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 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. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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: A188951 A226136 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

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Last modified May 30 18:38 EDT 2020. Contains 334728 sequences. (Running on oeis4.)