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

0,2

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).

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)

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A141586 A141758 A137496 * A051781 A077562 A307003

Adjacent sequences: A195012 A195013 A195014 * A195016 A195017 A195018

Keyword

nonn,easy

Author

Omar E. Pol, Sep 26 2011

Status

approved