|
|
A166151
|
|
a(n) = (5*n^2 + 5*n - 6)/2.
|
|
2
|
|
|
2, 12, 27, 47, 72, 102, 137, 177, 222, 272, 327, 387, 452, 522, 597, 677, 762, 852, 947, 1047, 1152, 1262, 1377, 1497, 1622, 1752, 1887, 2027, 2172, 2322, 2477, 2637, 2802, 2972, 3147, 3327, 3512, 3702, 3897, 4097, 4302, 4512, 4727, 4947, 5172, 5402, 5637
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 5*n*(n+1)/2 - 3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-2-6*x+3*x^2)/(x-1)^3. (End)
E.g.f.: (1/2)*(5*x^2 + 10*x - 6)*exp(x) + 6. - G. C. Greubel, May 01 2016
Sum_{n>=1} 1/a(n) = 1/3 + (2*Pi/sqrt(145))*tan(sqrt(29/5)*Pi/2). - Amiram Eldar, Feb 20 2023
|
|
MATHEMATICA
|
Table[(5 n^2 + 5 n - 6)/2, {n, 50}] (* or *) CoefficientList[Series[(- 2 - 6 x + 3 x^2)/(x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{3, -3, 1}, {2, 12, 27}, 50] (* G. C. Greubel, May 01 2016 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|