A168108 a(n) = sum of natural numbers m such that n - 9 <= m <= n + 9.

45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, 399, 418, 437, 456, 475, 494, 513, 532, 551, 570, 589, 608, 627, 646, 665, 684, 703, 722, 741, 760, 779, 798, 817, 836, 855, 874, 893, 912, 931, 950, 969, 988, 1007, 1026, 1045, 1064

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) = (9 + n)*(10 + n)/2 = A000217(9+n) for 0 <= n <= 9, a(n) = a(n-1) + 19 for n >= 10.

G.f.: (45 - 80*x + 36*x^2 - x^11)/(1 - x)^3. - G. C. Greubel, Jul 13 2016

Mathematica

CoefficientList[Series[(45 - 80*x + 36*x^2 - x^11)/(1 - x)^3, {x, 0, 50}]
, x] (* G. C. Greubel, Jul 13 2016 *)
LinearRecurrence[{2, -1}, {45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190}, 60] (* Harvey P. Dale, Jan 24 2021 *)

Prog

(PARI) a(n)=if(n>9, 19*n, (n+9)*(n+10)/2) \\ Charles R Greathouse IV, Jul 13 2016

Crossrefs

Sequence in context: A062390 A167328 A116247 * A037042 A119208 A068812

Adjacent sequences: A168105 A168106 A168107 * A168109 A168110 A168111

Keyword

nonn,easy

Author

Jaroslav Krizek, Nov 18 2009

Status

approved