A195047 Concentric 17-gonal numbers.

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

Author

Omar E. Pol, Sep 27 2011

Keywords

• nonn
• easy

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).

Crossrefs

Column 17 of A195040.

Cf. A032527, A032528, A061925, A069130, A151978, A195046, A195048, A195146, A195147.

Programs

Mathematica

LinearRecurrence[{2,0,-2,1},{0,1,17,35},50] (* Harvey P. Dale, Dec 23 2017 *)

PARI

a(n)=17*n^2/4+13*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015

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