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A168106 a(n) = sum of natural numbers m such that n - 7 <= m <= n + 7. 1

%I #13 Jun 30 2023 15:05:36

%S 28,36,45,55,66,78,91,105,120,135,150,165,180,195,210,225,240,255,270,

%T 285,300,315,330,345,360,375,390,405,420,435,450,465,480,495,510,525,

%U 540,555,570,585,600,615,630,645,660,675,690,705,720,735,750,765,780,795,810,825,840,855

%N a(n) = sum of natural numbers m such that n - 7 <= m <= n + 7.

%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="/A168106/b168106.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) = (7 + n)*(8 + n)/2 = A000217(7+n) for 0 <= n <= 7, a(n) = a(n-1) + 15 for n >= 8.

%F G.f.: (28 - 48*x + 21*x^2 - x^9)/(1 - x)^3. - _G. C. Greubel_, Jul 13 2016

%t CoefficientList[Series[(28 - 48*x + 21*x^2 - x^9)/(1 - x)^3, {x, 0, 25}], x] (* _G. C. Greubel_, Jul 13 2016 *)

%K nonn

%O 0,1

%A _Jaroslav Krizek_, Nov 18 2009

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)