The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A195032 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A195032

Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [5, 12, 13]. The edges of the spiral have length A195031.
(history; published version)

#40 by Charles R Greathouse IV at Thu Sep 08 08:45:59 EDT 2022

PROG

(MAGMAMagma) [(2*n*(17*n+27)+(14*n-3)*(-1)^n+3)/16: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#39 by Bruno Berselli at Fri Nov 23 03:30:05 EST 2018

STATUS

proposed

approved

#38 by G. C. Greubel at Fri Nov 23 02:38:04 EST 2018

STATUS

editing

proposed

#37 by G. C. Greubel at Fri Nov 23 02:37:45 EST 2018

PROG

(PARI) vector(50, n, n--; (2*n*(17*n+27)+(14*n-3)*(-1)^n+3)/16) \\ G. C. Greubel, Nov 23 2018

(Sage) [(2*n*(17*n+27)+(14*n-3)*(-1)^n+3)/16 for n in range(50)] # G. C. Greubel, Nov 23 2018

STATUS

proposed

editing

#36 by Amiram Eldar at Fri Nov 23 00:43:26 EST 2018

STATUS

editing

proposed

#35 by Amiram Eldar at Fri Nov 23 00:43:21 EST 2018

MATHEMATICA

a[n_] := (2 n (17 n + 27) + (14 n - 3)*(-1)^n + 3)/16; Array[a, 50, 0] (* Amiram Eldar, Nov 23 2018 *)

STATUS

proposed

editing

#34 by Franck Maminirina Ramaharo at Fri Nov 23 00:40:49 EST 2018

STATUS

editing

proposed

#33 by Franck Maminirina Ramaharo at Fri Nov 23 00:40:36 EST 2018

FORMULA

G.f.: x*(5 + 12*x)/((1 + x)^2*(1 - x)^3).

a(n) = (1/2)*((2*n + (-1)^n + 3)/4)*((34*n - 3*(-1)^n+3)/4) = (2*n*(17*n + 27) + (14*n - 3)*(-1)^n + 3)/16.

E.g.f.: (1/16)*((3 + 88*x + 34*x^2)*exp(x) - (3 + 14*x)*exp(-x)). - Franck Maminirina Ramaharo, Nov 23 2018

STATUS

proposed

editing

#32 by Michel Marcus at Thu Nov 22 23:42:35 EST 2018

STATUS

editing

proposed

#31 by Michel Marcus at Thu Nov 22 23:42:30 EST 2018

FORMULA

G.f.: x*(5+12*x)/((1+x)^2*(1-x)^3).

a(n) = (1/2)*((2*n + (-1)^n + 3)/4)*((34*n - 3*(-1)^n+3)/4) = (2*n*(17*n+27) + (14*n-3)*(-1)^n + 3)/16.

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

STATUS

proposed

editing