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%I #15 Jun 30 2023 15:06:31
%S 36,45,55,66,78,91,105,120,136,153,170,187,204,221,238,255,272,289,
%T 306,323,340,357,374,391,408,425,442,459,476,493,510,527,544,561,578,
%U 595,612,629,646,663,680,697,714,731,748,765,782,799,816,833,850,867,884,901,918,935,952,969
%N a(n) = sum of natural numbers m such that n - 8 <= m <= n + 8.
%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).
%H G. C. Greubel, <a href="/A168107/b168107.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 a(n) = (8 + n)*(9 + n)/2 = A000217(8+n) for 0 <= n <= 8, a(n) = a(n-1) + 17 for n >= 9.
%F G.f.: (36 - 63*x + 28*x^2 - x^10)/(1 - x)^3. - _G. C. Greubel_, Jul 13 2016
%t CoefficientList[Series[(36 - 63*x + 28*x^2 - x^10)/(1 - x)^3, {x, 0, 50}], x] (* _G. C. Greubel_, Jul 13 2016 *)
%t Join[Table[((8+n)(9+n))/2,{n,0,8}],NestList[17+#&,153,80]] (* _Harvey P. Dale_, Apr 06 2019 *)
%K nonn
%O 0,1
%A _Jaroslav Krizek_, Nov 18 2009
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