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Multiples of 29.
8

%I #19 Apr 02 2024 21:45:59

%S 0,29,58,87,116,145,174,203,232,261,290,319,348,377,406,435,464,493,

%T 522,551,580,609,638,667,696,725,754,783,812,841,870,899,928,957,986,

%U 1015,1044,1073,1102,1131,1160,1189,1218,1247,1276,1305,1334

%N Multiples of 29.

%C Length of hypotenuses on the main diagonal of the Pythagorean spiral whose edges have length A195033 and whose vertices are the numbers A195034, if n >= 1.

%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 29*n.

%F From _Elmo R. Oliveira_, Mar 21 2024: (Start)

%F G.f.: 29*x/(x-1)^2.

%F E.g.f.: 29*x*exp(x).

%F a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

%t 29Range[0,50] (* _Harvey P. Dale_, Oct 25 2011 *)

%Y Cf. A004922, A004942, A008605, A010868, A135631, A195033, A195034.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Oct 12 2011