OFFSET
0,3
COMMENTS
Also concentric heptadecagonal numbers or concentric heptakaidecagonal numbers.
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
a(n) = 17*n^2/4+13*((-1)^n-1)/8. [Typo fixed by Ivan Panchenko, Nov 08 2013]
From R. J. Mathar, Sep 28 2011: (Start)
G.f.: -x*(1+15*x+x^2) / ( (1+x)*(x-1)^3 ).
a(n)+a(n+1) = A069130(n+1). (End)
From Bruno Berselli, Sep 29 2011: (Start)
a(n) = a(-n) = (34*n^2+13*(-1)^n-13)/8.
Sum_{n>=1} 1/a(n) = Pi^2/102 + tan(sqrt(13/17)*Pi/2)*Pi/sqrt(221). - Amiram Eldar, Jan 16 2023
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1}, {0, 1, 17, 35}, 50] (* Harvey P. Dale, Dec 23 2017 *)
PROG
(PARI) a(n)=17*n^2/4+13*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 27 2011
STATUS
approved