A195015 Main axis of the square spiral whose edges have length A195013 and whose vertices are the numbers A195014.

0, 2, 12, 24, 44, 66, 96, 128, 168, 210, 260, 312, 372, 434, 504, 576, 656, 738, 828, 920, 1020, 1122, 1232, 1344, 1464, 1586, 1716, 1848, 1988, 2130, 2280, 2432, 2592, 2754, 2924, 3096, 3276, 3458, 3648, 3840, 4040, 4242, 4452, 4664, 4884

Offset: 0

Author

Omar E. Pol, Sep 26 2011

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 0, in the direction 0, 2, ..., and the same line from 0, in the direction 0, 12, ..., in the square spiral mentioned above. Axis perpendicular to A195016 in the same spiral.

Also four times A005475 and positives A152965 interleaved.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A000566, A005475, A005476, A028895, A033571, A152965, A153126, A195013, A195014, A195016.

Programs

Magma

[(2*n*(5*n+2)+3*(-1)^n-3)/4: n in [0..50]]; // Vincenzo Librandi, Oct 28 2011

Mathematica

LinearRecurrence[{2, 0, -2, 1}, {0, 2, 12, 24}, 50] (* Paolo Xausa, Feb 09 2024 *)

Formula

From Bruno Berselli, Oct 14 2011: (Start)

G.f.: 2*x*(1+4*x)/((1+x)*(1-x)^3).

a(n) = (2*n*(5*n+2) + 3*(-1)^n-3)/4.

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

a(n) + a(n-1) = A135706(n). (End)