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 A168107 a(n) = sum of natural numbers m such that n - 8 <= m <= n + 8. 1
 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425, 442, 459, 476, 493, 510, 527, 544, 561, 578, 595, 612, 629, 646, 663, 680, 697, 714, 731, 748, 765, 782, 799, 816, 833, 850, 867, 884, 901, 918, 935, 952, 969 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n) = (8 + n)*(9 + n)/2 = A000217(8+n) for 0 <= n <= 8, a(n) = a(n-1) + 17 for n >= 9. G.f.: (36 - 63*x + 28*x^2 - x^10)/(1 - x)^3. - G. C. Greubel, Jul 13 2016 MATHEMATICA CoefficientList[Series[(36 - 63*x + 28*x^2 - x^10)/(1 - x)^3, {x, 0, 50}], x] (* G. C. Greubel, Jul 13 2016 *) Join[Table[((8+n)(9+n))/2, {n, 0, 8}], NestList[17+#&, 153, 80]] (* Harvey P. Dale, Apr 06 2019 *) CROSSREFS Sequence in context: A138566 A062034 A250641 * A048034 A195528 A144291 Adjacent sequences: A168104 A168105 A168106 * A168108 A168109 A168110 KEYWORD nonn AUTHOR Jaroslav Krizek, Nov 18 2009 STATUS approved

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Last modified June 2 01:13 EDT 2023. Contains 363078 sequences. (Running on oeis4.)