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

28, 36, 45, 55, 66, 78, 91, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, 765, 780, 795, 810, 825, 840, 855

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

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

Formula

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

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

Mathematica

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

Crossrefs

Sequence in context: A043950 A167308 A303261 * A061900 A048023 A359529

Adjacent sequences: A168103 A168104 A168105 * A168107 A168108 A168109

Keyword

nonn

Author

Jaroslav Krizek, Nov 18 2009

Status

approved