A174371 a(n) = (6*n-1)^2.

1, 25, 121, 289, 529, 841, 1225, 1681, 2209, 2809, 3481, 4225, 5041, 5929, 6889, 7921, 9025, 10201, 11449, 12769, 14161, 15625, 17161, 18769, 20449, 22201, 24025, 25921, 27889, 29929, 32041, 34225, 36481, 38809, 41209, 43681, 46225, 48841, 51529

Offset: 0

Author

Juri-Stepan Gerasimov, Mar 17 2010

Keywords

• nonn
• easy

Comments

Unit together with numbers of form (6*n+5)^2.

Sequence may be obtained by starting with the segment (1, 25) followed by the line from 25 in the direction 25, 121,... in the square spiral whose vertices are the generalized 20-gonal numbers. - Omar E. Pol, Jul 29 2016

Examples

			a(0)=1 because (6*0-1)^2=1, a(1)=25 because (6*1-1)^2=25.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A016970, A033579.

Programs

Magma

[(6*n-1)^2: n in [0..50]]; // Vincenzo Librandi, May 07 2011

Mathematica

CoefficientList[Series[(49*x^2 + 22*x + 1)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 27 2013 *)

PARI

a(n)=(6*n-1)^2 \\ Charles R Greathouse IV, Jul 28 2016

Formula

a(n) = A016970(n-1), n >= 1.

G.f.: (49*x^2 + 22*x + 1)/(1 - x)^3. - Vincenzo Librandi, Jan 27 2013

a(n) = 6*A033579(n) + 1. - Miquel Cerda, Jul 28 2016

a(n) = 36n^2 - 12n + 1. - Omar E. Pol, Jul 28 2016

E.g.f.: exp(x)*(1 + 24*x + 36*x^2). - Stefano Spezia, Aug 19 2023

Extensions

Offset and formula corrected by R. J. Mathar, Apr 16 2010