

A195027


a(n) = 2*n*(7*n + 5).


3



0, 24, 76, 156, 264, 400, 564, 756, 976, 1224, 1500, 1804, 2136, 2496, 2884, 3300, 3744, 4216, 4716, 5244, 5800, 6384, 6996, 7636, 8304, 9000, 9724, 10476, 11256, 12064, 12900, 13764, 14656, 15576, 16524, 17500, 18504, 19536, 20596, 21684, 22800
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OFFSET

0,2


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 24, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semiaxis opposite to A195023 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 14*n^2 + 10*n.
a(n) = 4*A179986(n).  Bruno Berselli, Oct 13 2011
G.f.: 4*x*(6+x)/(1x)^3.  Colin Barker, Jan 09 2012
a(n) = 3*a(n1)  3*a(n2) + a(n3); a(0)=0, a(1)=24, a(2)=76.  Harvey P. Dale, Jul 24 2012


MATHEMATICA

Table[2n(7n+5), {n, 0, 50}] (* or *) LinearRecurrence[{3, 3, 1}, {0, 24, 76}, 50] (* Harvey P. Dale, Jul 24 2012 *)


PROG

(MAGMA) [14*n^2 +10*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=2*n*(7*n+5) \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A144555, A152760, A179986, A195019, A195020, A195021, A195023, A195024, A195025, A195026, A195320.
Cf. A185019, A193053, A198017.
Sequence in context: A033572 A233883 A291630 * A325958 A211574 A211588
Adjacent sequences: A195024 A195025 A195026 * A195028 A195029 A195030


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Oct 13 2011


STATUS

approved



