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

1,2

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).

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)

Mathematica

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

Prog

(Magma) [(14*n^2-14*n+1): n in [1..50]]; // Vincenzo Librandi, Sep 19 2011
(PARI) a(n)=14*n^2-14*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Bisection of A195145.

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

Cf. A069127, A118277, A144555.

Sequence in context: A343683 A255187 A273362 * A323218 A124784 A126383

Adjacent sequences: A195311 A195312 A195313 * A195315 A195316 A195317

Keyword

nonn,easy

Author

Omar E. Pol, Sep 16 2011

Status

approved