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

0,3

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).

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

Mathematica

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

Prog

(Magma) [11*n^2/4+7*((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 30 2011
(Haskell)
a195043 n = a195043_list !! n
a195043_list = scanl (+) 0 a175885_list
-- Reinhard Zumkeller, Jan 07 2012
(PARI) Vec(-x*(x^2+9*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Sep 15 2013

Crossrefs

Column 11 of A195040.

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

Sequence in context: A228444 A191235 A146451 * A029468 A198588 A334829

Adjacent sequences: A195040 A195041 A195042 * A195044 A195045 A195046

Keyword

nonn,easy

Author

Omar E. Pol, Sep 27 2011

Status

approved