|
| |
|
|
A082109
|
|
Third row of number array A082105.
|
|
12
|
|
|
|
1, 13, 33, 61, 97, 141, 193, 253, 321, 397, 481, 573, 673, 781, 897, 1021, 1153, 1293, 1441, 1597, 1761, 1933, 2113, 2301, 2497, 2701, 2913, 3133, 3361, 3597, 3841, 4093, 4353, 4621, 4897, 5181, 5473, 5773, 6081, 6397, 6721, 7053, 7393, 7741, 8097, 8461
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Define b(n) = A000217(n), the triangular numbers. Using six consecutive terms to create the vertices of a triangle at points (b(n-2), b(n-1)), (b(n), b(n+1)), and (b(n+2), b(n+3)), one fourth the area of these triangles = a(n). - J. M. Bergot, Jul 30 2013
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = 4*n^2 + 8*n + 1.
Sum_{n>=0} 1/a(n) = 1/6 - cot(sqrt(3)*Pi/2)*sqrt(3)*Pi/12.
Sum_{n>=0} (-1)^n/a(n) = cosec(sqrt(3)*Pi/2)*sqrt(3)*Pi/12 - 1/6. (End)
|
|
|
MATHEMATICA
|
|
|
|
PROG
|
(Magma) [4*n^2+8*n+1: n in [0..60]]; // G. C. Greubel, Dec 22 2022
(SageMath) [4*n^2+8*n+1 for n in range(61)] # G. C. Greubel, Dec 22 2022
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
