A195043 Concentric 11-gonal numbers.

0, 1, 11, 23, 44, 67, 99, 133, 176, 221, 275, 331, 396, 463, 539, 617, 704, 793, 891, 991, 1100, 1211, 1331, 1453, 1584, 1717, 1859, 2003, 2156, 2311, 2475, 2641, 2816, 2993, 3179, 3367, 3564, 3763, 3971, 4181, 4400, 4621, 4851, 5083, 5324, 5567

Offset: 0

Author

Omar E. Pol, Sep 27 2011

Keywords

• nonn
• easy

Comments

Also concentric hendecagonal numbers. A033584 and A069173 interleaved.

Partial sums of A175885. - Reinhard Zumkeller, Jan 07 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Column 11 of A195040.

Cf. A032527, A032528, A033584, A069173, A175885, A195042, A195142, A195143, A195045.

Programs

Haskell

a195043 n = a195043_list !! n
a195043_list = scanl (+) 0 a175885_list
-- Reinhard Zumkeller, Jan 07 2012

Magma

[11*n^2/4+7*((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 30 2011

Mathematica

LinearRecurrence[{2,0,-2,1},{0,1,11,23},50] (* Harvey P. Dale, May 20 2019 *)

PARI

Vec(-x*(x^2+9*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Sep 15 2013

Formula

a(n) = 11*n^2/4 + 7*((-1)^n - 1)/8.

a(n) = -a(n-1) + A069125(n). - Vincenzo Librandi, Sep 30 2011

From Colin Barker, Sep 15 2013: (Start)

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

G.f.: -x*(x^2+9*x+1) / ((x-1)^3*(x+1)). (End)

Sum_{n>=1} 1/a(n) = Pi^2/66 + tan(sqrt(7/11)*Pi/2)*Pi/sqrt(77). - Amiram Eldar, Jan 16 2023