A195033 Multiples of 21 and of 20 interleaved: a(2n-1) = 21n, a(2n) = 20n.

21, 20, 42, 40, 63, 60, 84, 80, 105, 100, 126, 120, 147, 140, 168, 160, 189, 180, 210, 200, 231, 220, 252, 240, 273, 260, 294, 280, 315, 300, 336, 320, 357, 340, 378, 360, 399, 380, 420, 400, 441, 420, 462, 440, 483, 460, 504, 480, 525, 500, 546, 520, 567, 540

Offset: 1

Author

Omar E. Pol, Sep 12 2011

Keywords

• nonn
• easy

Comments

First differences of A195034.

a(n) is also the length of the n-th edge of a square spiral in which the first two edges are the legs of the primitive Pythagorean triple [21, 20, 29]. Zero together with partial sums give A195034, the vertices of the spiral.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Ron Knott, Pythagorean triangles and Triples
• Eric Weisstein's World of Mathematics, Pythagorean Triple
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A010693, A010718, A029578.

Cf. A195019, A195031, A195034, A195035.

Programs

Magma

&cat[[21*n,20*n]: n in [1..27]];  // Bruno Berselli, Sep 29 2011

Mathematica

Riffle[21*#, 20*#] & [Range[50]] (* Paolo Xausa, Mar 21 2024 *)

PARI

a(n)=(n+1)\2*if(n%2,21,20) \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Bruno Berselli, Sep 29 2011: (Start)

G.f.: x*(21+20*x)/((1-x)^2*(1+x)^2).

a(n) = A010693(n)*A010718(n)*A029578(n+1) = (41*n-(n+21)*(-1)^n+21)/4.

a(n) = 2*a(n-2) - a(n-4). (End)

Extensions

More terms from Bruno Berselli, Sep 29 2011