A168104 a(n) = sum of natural numbers m such that n - 5 <= m <= n + 5.

15, 21, 28, 36, 45, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583, 594, 605, 616, 627

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). a(n) = (5 + n)*(6 + n)/2 = A000217(5+n) for 0 <= n <= 5, a(n) = a(n-1) + 11 for n >= 6.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, -1).

Formula

G.f.: (15 - 24*x + 10*x^2 - x^7)/(1 - x)^3. - G. C. Greubel, Jul 12 2016

Mathematica

CoefficientList[Series[(15  - 24*x + 10*x^2 - x^7)/(1 - x)^3, {x, 0, 25}] , x] (* G. C. Greubel, Jul 12 2016 *)

Crossrefs

Sequence in context: A226025 A082686 A102030 * A026048 A195527 A047200

Adjacent sequences: A168101 A168102 A168103 * A168105 A168106 A168107

Keyword

nonn

Author

Jaroslav Krizek, Nov 18 2009

Status

approved