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 A168103 a(n) = sum of natural numbers m such that n - 4 <= m <= n + 4. 1

%I

%S 10,15,21,28,36,45,54,63,72,81,90,99,108,117,126,135,144,153,162,171,

%T 180,189,198,207,216,225,234,243,252,261,270,279,288,297,306,315,324,

%U 333,342,351,360,369,378,387,396,405,414,423,432,441,450,459,468,477,486,495,504,513,522

%N a(n) = sum of natural numbers m such that n - 4 <= m <= n + 4.

%C a(n) = a(n-1) + 9 for n >= 5. 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) = (4 + n)*(5 + n)/2 = A000217(4+n) for 0 <= n <= 4, a(n) = a(n-1) + 9 for n >= 5.

%H G. C. Greubel, <a href="/A168103/b168103.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (10 - 15*x + 6*x^2 - x^6)/(1 - x)^3. - _G. C. Greubel_, Jul 12 2016

%t CoefficientList[Series[(10 - 15*x + 6*x^2 - x^6)/(1 - x)^3, {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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Last modified December 9 02:23 EST 2021. Contains 349624 sequences. (Running on oeis4.)