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A174371
a(n) = (6*n-1)^2.
3
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
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
Sequence in context: A363190 A031151 A016970 * A062938 A361637 A190875
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Offset and formula corrected by R. J. Mathar, Apr 16 2010
STATUS
approved