A195320 - OEIS

%I #31 Sep 08 2022 08:45:59

%S 0,7,42,105,196,315,462,637,840,1071,1330,1617,1932,2275,2646,3045,

%T 3472,3927,4410,4921,5460,6027,6622,7245,7896,8575,9282,10017,10780,

%U 11571,12390,13237,14112,15015,15946,16905,17892,18907,19950,21021,22120,23247,24402

%N 7 times hexagonal numbers: 7*n*(2*n-1).

%C Sequence found by reading the line from 0, in the direction 0, 7, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277.

%C Also sequence found by reading the same line (mentioned above) in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-diagonals of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5]. - _Omar E. Pol_, Oct 13 2011

%H Vincenzo Librandi, <a href="/A195320/b195320.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 14*n^2 - 7*n = 7*A000384(n).

%F G.f.: -7*x*(1+3*x) / (x-1)^3. - _R. J. Mathar_, Sep 27 2011

%o (Magma) [7*n*(2*n-1): n in [0..50]]; // _Vincenzo Librandi_, Sep 28 2011

%o (PARI) a(n)=7*n*(2*n-1) \\ _Charles R Greathouse IV_, Sep 28 2015

%Y Bisection of A024966.

%Y Cf. A000384, A118277, A152746, A152750, A185019, A193053, A198017.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Sep 18 2011