A195042 Concentric 9-gonal numbers.

0, 1, 9, 19, 36, 55, 81, 109, 144, 181, 225, 271, 324, 379, 441, 505, 576, 649, 729, 811, 900, 991, 1089, 1189, 1296, 1405, 1521, 1639, 1764, 1891, 2025, 2161, 2304, 2449, 2601, 2755, 2916, 3079, 3249, 3421, 3600, 3781, 3969, 4159, 4356, 4555, 4761, 4969, 5184, 5401, 5625

Offset

0,3

Comments

Also concentric enneagonal numbers or concentric nonagonal numbers.

A016766 and A069131 interleaved.

Partial sums of A056020. - 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) = (9*n^2 + 5/2*((-1)^n - 1))/4.

From R. J. Mathar, Sep 28 2011: (Start)

G.f.: -x*(1+7*x+x^2) / ( (1+x)*(x-1)^3 ).

a(n) + a(n+1) = A060544(n+1). (End)

Sum_{n>=1} 1/a(n) = Pi^2/54 + tan(sqrt(5)*Pi/6)*Pi/(3*sqrt(5)). - Amiram Eldar, Jan 16 2023

Mathematica

LinearRecurrence[{2, 0, -2, 1}, {0, 1, 9, 19}, 60] (* Harvey P. Dale, Nov 24 2019 *)

Prog

(Magma) [(9*n^2+5/2*((-1)^n-1))/4: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011
(Haskell)
a195042 n = a195042_list !! n
a195042_list = scanl (+) 0 a056020_list
-- Reinhard Zumkeller, Jan 07 2012
(PARI) a(n)=(9*n^2+5/2*((-1)^n-1))/4 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Column 9 of A195040.

Cf. A016766, A069131, A077221, A195041, A195142, A195043.

Sequence in context: A274590 A051811 A034056 * A157034 A198590 A297396

Adjacent sequences: A195039 A195040 A195041 * A195043 A195044 A195045

Keyword

nonn,easy

Author

Omar E. Pol, Sep 27 2011

Status

approved