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

0,3

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.

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

E.g.f.: (17*x*(x + 1)*cosh(x) + (17*x^2 + 17*x - 13)*sinh(x))/4. - Elmo R. Oliveira, Jun 19 2026

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

Column 17 of A195040.

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

Sequence in context: A004921 A239129 A212427 * A198587 A385110 A041570

Adjacent sequences: A195044 A195045 A195046 * A195048 A195049 A195050

Keyword

nonn,easy

Author

Omar E. Pol, Sep 27 2011

Status

approved