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A195043
Concentric 11-gonal numbers.
7
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
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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 27 2011
STATUS
approved