

A201279


a(n) = 6n^2 + 10n + 5.


5



5, 21, 49, 89, 141, 205, 281, 369, 469, 581, 705, 841, 989, 1149, 1321, 1505, 1701, 1909, 2129, 2361, 2605, 2861, 3129, 3409, 3701, 4005, 4321, 4649, 4989, 5341, 5705, 6081, 6469, 6869, 7281, 7705, 8141, 8589, 9049, 9521, 10005, 10501, 11009, 11529, 12061
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OFFSET

0,1


COMMENTS

Numbers n where 6n5 is a square of a number type 6n1.
Also sequence found by reading the line from 5, in the direction 5, 21,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318.  Omar E. Pol, Jul 18 2012
The spiral mentioned above naturally appears on a "graphene" like lattice (planar net 6^3). The opposite diagonal is A080859.  Yuriy Sibirmovsky, Oct 04 2016
First differences of A048395.  Leo Tavares, Nov 24 2021 [Corrected by Omar E. Pol, Dec 26 2021]


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Yuriy Sibirmovsky, Diagonals of a 'graphene' number spiral.
Leo Tavares, Illustration: Diamond Frame Stars
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: (1+x)*(5+x)/(1x)^3.  Colin Barker, Jan 09 2012
a(n) = 1 + A033579(n+1).  Omar E. Pol, Jul 18 2012
a(n) = (n+1)*A001844(n+1)n*A001844(n). [Bruno Berselli, Jan 15 2013]
From Leo Tavares, Nov 24 2021: (Start)
a(n) = A003154(n+2)  A022144(n+1). See Diamond Frame Stars illustration.
a(n) = A016754(n) + A046092(n+1). (End)


MATHEMATICA

LinearRecurrence[{3, 3, 1}, {5, 21, 49}, 50] (* Vincenzo Librandi, Dec 01 2011 *)
Table[6 n^2 + 10 n + 5, {n, 0, 44}] (* or *)
CoefficientList[Series[(1 + x) (5 + x)/(1  x)^3, {x, 0, 44}], x] (* Michael De Vlieger, Oct 04 2016 *)


PROG

(PARI) a(n)=6*n^2+10*n+5 \\ Charles R Greathouse IV, Nov 29 2011
(Magma) [6*n^2 + 10*n + 5: n in [0..60]]; // Vincenzo Librandi, Dec 01 2011


CROSSREFS

Cf. A136392, A080859.
Cf. A003154, A022144, A016754, A046092, A048395.
Sequence in context: A296200 A041825 A022268 * A146721 A099979 A039659
Adjacent sequences: A201276 A201277 A201278 * A201280 A201281 A201282


KEYWORD

nonn,easy


AUTHOR

Eleonora EcheverriToro, Nov 29 2011


STATUS

approved



