A168109 a(n) = sum of natural numbers m such that n - 10 <= m <= n + 10.

55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092, 1113, 1134, 1155

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) = (10 + n)*(11 + n)/2 = A000217(10+n) for 0 <= n <= 10, a(n) = a(n-1) + 21 for n >= 11.

Links

Table of n, a(n) for n=0..55.

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

Formula

G.f.: (55 - 99*x + 45*x^2 - x^12)/(1 - x)^3. - G. C. Greubel, Jul 13 2016

Mathematica

CoefficientList[Series[(55 - 99*x + 45*x^2 - x^12)/(1 - x)^3, {x, 0, 50}] , x] (* G. C. Greubel, Jul 13 2016 *)

Prog

(PARI) a(n)=if(n>9, 21*n, (n+10)*(n+11)/2) \\ Charles R Greathouse IV, Jul 13 2016

Crossrefs

Sequence in context: A285804 A269808 A004434 * A116055 A068898 A068899

Adjacent sequences: A168106 A168107 A168108 * A168110 A168111 A168112

Keyword

nonn,easy

Author

Jaroslav Krizek, Nov 18 2009

Status

approved