OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 21,..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-diagonal opposite to A195320 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
Sum of the numbers from 6n to 8n. - Wesley Ivan Hurt, Dec 23 2015
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 + 7*n.
a(n) = 7*A014105(n). - Bruno Berselli, Oct 13 2011
From Colin Barker, Apr 09 2012: (Start)
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
G.f.: 7*x*(3+x)/(1-x)^3. (End)
a(n) = Sum_{i=6n..8n} i. - Wesley Ivan Hurt, Dec 23 2015
MAPLE
MATHEMATICA
Table[7*n*(2*n + 1), {n, 0, 50}] (* Wesley Ivan Hurt, Dec 23 2015 *)
LinearRecurrence[{3, -3, 1}, {0, 21, 70}, 50] (* Harvey P. Dale, Apr 26 2017 *)
PROG
(Magma) [14*n^2 +7*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=7*n*(2*n+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 13 2011
STATUS
approved