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

0,2

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Example

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

Mathematica

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

Prog

(Magma) [(6*n-1)^2: n in [0..50]]; // Vincenzo Librandi, May 07 2011
(PARI) a(n)=(6*n-1)^2 \\ Charles R Greathouse IV, Jul 28 2016

Crossrefs

Cf. A016970, A033579.

Sequence in context: A363190 A031151 A016970 * A062938 A361637 A190875

Adjacent sequences: A174368 A174369 A174370 * A174372 A174373 A174374

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Mar 17 2010

Extensions

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

Status

approved