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A168103
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a(n) = sum of natural numbers m such that n - 4 <= m <= n + 4.
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1
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10, 15, 21, 28, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f.: (10 - 15*x + 6*x^2 - x^6)/(1 - x)^3. - G. C. Greubel, Jul 12 2016
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MATHEMATICA
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CoefficientList[Series[(10 - 15*x + 6*x^2 - x^6)/(1 - x)^3, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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