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A195047
Concentric 17-gonal numbers.
7
0, 1, 17, 35, 68, 103, 153, 205, 272, 341, 425, 511, 612, 715, 833, 953, 1088, 1225, 1377, 1531, 1700, 1871, 2057, 2245, 2448, 2653, 2873, 3095, 3332, 3571, 3825, 4081, 4352, 4625, 4913, 5203, 5508, 5815, 6137, 6461, 6800, 7141, 7497, 7855, 8228, 8603, 8993
OFFSET
0,3
COMMENTS
Also concentric heptadecagonal numbers or concentric heptakaidecagonal numbers.
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.
a(n) = A151978(A061925(n)). (End)
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