A168103 a(n) = sum of natural numbers m such that n - 4 <= m <= n + 4.

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

Offset

0,1

Comments

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.

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.: (10 - 15*x + 6*x^2 - x^6)/(1 - x)^3. - G. C. Greubel, Jul 12 2016

Mathematica

CoefficientList[Series[(10  - 15*x + 6*x^2 - x^6)/(1 - x)^3, {x, 0, 25}], x] (* G. C. Greubel, Jul 12 2016 *)
LinearRecurrence[{2, -1}, {10, 15, 21, 28, 36, 45}, 60] (* Harvey P. Dale, Dec 10 2024 *)

Crossrefs

Sequence in context: A068992 A325901 A098564 * A322045 A062691 A257630

Adjacent sequences: A168100 A168101 A168102 * A168104 A168105 A168106

Keyword

nonn

Author

Jaroslav Krizek, Nov 18 2009

Status

approved