A195145 Concentric 14-gonal numbers.

0, 1, 14, 29, 56, 85, 126, 169, 224, 281, 350, 421, 504, 589, 686, 785, 896, 1009, 1134, 1261, 1400, 1541, 1694, 1849, 2016, 2185, 2366, 2549, 2744, 2941, 3150, 3361, 3584, 3809, 4046, 4285, 4536, 4789, 5054, 5321, 5600, 5881, 6174, 6469, 6776, 7085, 7406

Offset

0,3

Comments

Also concentric tetradecagonal numbers or concentric tetrakaidecagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 14, ..., and the same line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Main axis, perpendicular to A024966 in the same spiral.

Partial sums of A113801. - 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

G.f.: -x*(1+12*x+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Sep 18 2011

From Vincenzo Librandi, Sep 27 2011: (Start)

a(n) = (14*n^2 + 5*(-1)^n - 5)/4;

a(n) = a(-n) = -a(n-1) + 7*n^2 - 7*n + 1. (End)

Sum_{n>=1} 1/a(n) = Pi^2/84 + tan(sqrt(5/7)*Pi/2)*Pi/(2*sqrt(35)). - Amiram Eldar, Jan 16 2023

Mathematica

LinearRecurrence[{2, 0, -2, 1}, {0, 1, 14, 29}, 50] (* Amiram Eldar, Jan 16 2023 *)

Prog

(Magma) [(14*n^2+5*(-1)^n-5)/4: n in [0..50]]; // Vincenzo Librandi, Sep 27 2011
(Haskell)
a195145 n = a195145_list !! n
a195145_list = scanl (+) 0 a113801_list
-- Reinhard Zumkeller, Jan 07 2012

Crossrefs

A144555 and A195314 interleaved.

Cf. A024966, A032527, A032528, A077221, A113801, A195045, A195046, A195142, A195143, A195146, A195147, A195148, A195149.

Column 14 of A195040. - Omar E. Pol, Sep 28 2011

Sequence in context: A132756 A192836 A124681 * A263119 A196305 A041386

Adjacent sequences: A195142 A195143 A195144 * A195146 A195147 A195148

Keyword

nonn,easy

Author

Omar E. Pol, Sep 17 2011

Status

approved