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%I #10 Jun 30 2023 14:32:42
%S 3,6,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,
%T 110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,
%U 195,200,205,210,215,220,225,230,235,240,245,250,255,260,265,270,275,280,285,290,295,300,305
%N a(n) = sum of natural numbers m such that n - 2 <= m <= n + 2.
%C Generalization: If a(n,k) = sum of natural numbers m such that n - k <= m <= n + k (k >= 1) then a(n,k) = (k + n)*(k + n + 1)/2 = A000217(k+n) for 0 <= n <= k, a(n,k) = a(n-1,k) +2k + 1 = ((k + n - 1)*(k + n)/2) + 2k + 1 = A000217(k+n-1) +2k +1 for n >= k + 1 (see, e.g., A008486). a(n) = (2 + n)*(3 + n)/2 = A000217(2+n) for 0 <= n <= 2, a(n) = a(n-1) + 5 for n >= 3.
%H G. C. Greubel, <a href="/A168101/b168101.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F G.f.: (3 + x^2 + x^3)/(1 - x)^2. - _G. C. Greubel_, Jul 12 2016
%t CoefficientList[Series[(3 + x^2 + x^3)/(1 - x)^2, {x, 0, 25}], x] (* _G. C. Greubel_, Jul 12 2016 *)
%K nonn
%O 0,1
%A _Jaroslav Krizek_, Nov 18 2009
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