The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A069072 a(n) = (2n+1)*(2n+2)*(2n+3). 8
 6, 60, 210, 504, 990, 1716, 2730, 4080, 5814, 7980, 10626, 13800, 17550, 21924, 26970, 32736, 39270, 46620, 54834, 63960, 74046, 85140, 97290, 110544, 124950, 140556, 157410, 175560, 195054, 215940, 238266, 262080, 287430, 314364, 342930 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Terms are areas of primitive Pythagorean triangles whose odd sides differ by 2; e.g., the triangle with sides 8,15,17 has area 60. - Lekraj Beedassy, Apr 18 2003 Using (n, n+1), (n, n+2), and (n+1, n+2) to generate three unreduced Pythagorean triangles gives a sum of the areas for all three to be (2*n+1)*(2*n+2)*(2*n+3), which are three consecutive numbers. - J. M. Bergot, Aug 22 2011 REFERENCES T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 190. Jolley, Summation of Series, Oxford (1961). Konrad Knopp, Theory and application of infinite series, Dover, p. 269. LINKS M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013 Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series") S. Ramanujan, Notebook entry Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA log(2) - 1/2 = sum_{n>=0}, 1/a(n); (1/2)*(1-log(2)) = sum_{n>=0} (-1)^n/a(n). [Jolley eq 236 and 237] sum_{n>=0} x^n/a(n) = ((1+x)/sqrt(x)*log((1+sqrt x)/(1-sqrt x)) + 2*log(1-x)-2)/(4x). [Jolley eq 280 for 0=0} (-x)^n/a(n) = (1-log(1+x) -(1-x)/sqrt(x)*arctan(x))/(2x). [Jolley eq 281 for 0

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)