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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
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. Semi-axis opposite to A195023 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
FORMULA
a(n) = 14*n^2 + 10*n.
a(n) = 4*A179986(n). - Bruno Berselli, Oct 13 2011
G.f.: 4*x*(6+x)/(1-x)^3. - Colin Barker, Jan 09 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); 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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 13 2011
STATUS
approved