A195158 Concentric 24-gonal numbers.

0, 1, 24, 49, 96, 145, 216, 289, 384, 481, 600, 721, 864, 1009, 1176, 1345, 1536, 1729, 1944, 2161, 2400, 2641, 2904, 3169, 3456, 3745, 4056, 4369, 4704, 5041, 5400, 5761, 6144, 6529, 6936, 7345, 7776, 8209, 8664, 9121, 9600, 10081, 10584, 11089

Offset

0,3

Comments

Sequence found by reading the line from 0, in the direction 0, 24, ..., and the same line from 1, in the direction 1, 49, ..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818. Main axis, perpendicular to A049598 in the same spiral.

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) = 6*n^2 + 5*((-1)^n-1)/2.

a(n) = -a(n-1) + A069190(n). - Vincenzo Librandi, Sep 30 2011

From Colin Barker, Sep 16 2012: (Start)

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

G.f.: x*(1+22*x+x^2)/((1-x)^3*(1+x)). (End)

Sum_{n>=1} 1/a(n) = Pi^2/144 + tan(sqrt(5/6)*Pi/2)*Pi/(4*sqrt(30)). - Amiram Eldar, Jan 17 2023

Mathematica

LinearRecurrence[{2, 0, -2, 1}, {0, 1, 24, 49}, 50] (* Harvey P. Dale, Jan 28 2021 *)

Prog

(Magma) [(12*n^2+5*(-1)^n-5)/2: n in [0..50]]; // Vincenzo Librandi, Sep 30 2011
(PARI) a(n)=6*n^2+5*((-1)^n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Column 24 of A195040.

Cf. A032527, A032528, A195143, A195149, A195058.

Sequence in context: A044482 A045294 A258366 * A045279 A042142 A042144

Adjacent sequences: A195155 A195156 A195157 * A195159 A195160 A195161

Keyword

nonn,easy

Author

Omar E. Pol, Sep 28 2011

Status

approved