A195314 Centered 28-gonal numbers.

1, 29, 85, 169, 281, 421, 589, 785, 1009, 1261, 1541, 1849, 2185, 2549, 2941, 3361, 3809, 4285, 4789, 5321, 5881, 6469, 7085, 7729, 8401, 9101, 9829, 10585, 11369, 12181, 13021, 13889, 14785, 15709, 16661, 17641, 18649, 19685, 20749, 21841, 22961, 24109, 25285, 26489

Offset: 1

Author

Omar E. Pol, Sep 16 2011

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Semi-axis opposite to A144555 in the same spiral.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Bisection of A195145.

Cf. A003154, A069129, A069133, A069190, A195315, A195316, A195317, A195318.

Cf. A069127, A118277, A144555.

Programs

Magma

[(14*n^2-14*n+1): n in [1..50]]; // Vincenzo Librandi, Sep 19 2011

Mathematica

Table[14n^2-14n+1,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,29,85},50]

PARI

a(n)=14*n^2-14*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 14*n^2 - 14*n + 1.

G.f.: -x*(1 + 26*x + x^2)/(x-1)^3. - R. J. Mathar, Sep 18 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Oct 01 2011

Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(5/7)*Pi/2)/(2*sqrt(35)). - Amiram Eldar, Feb 11 2022

From Elmo R. Oliveira, Nov 14 2024: (Start)

E.g.f.: exp(x)*(14*x^2 + 1) - 1.

a(n) = 2*A069127(n) - 1. (End)