A195031 Multiples of 5 and of 12 interleaved: a(2n-1) = 5n, a(2n) = 12n.

5, 12, 10, 24, 15, 36, 20, 48, 25, 60, 30, 72, 35, 84, 40, 96, 45, 108, 50, 120, 55, 132, 60, 144, 65, 156, 70, 168, 75, 180, 80, 192, 85, 204, 90, 216, 95, 228, 100, 240, 105, 252, 110, 264, 115, 276, 120, 288, 125, 300, 130, 312, 135, 324, 140, 336, 145, 348

Offset: 1

Author

Omar E. Pol, Sep 12 2011

Keywords

• nonn
• easy

Comments

First differences of A195032.

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 [5, 12, 13]. Zero together with partial sums give A195032, 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. A195019, A195032, A195033, A195035.

Programs

Magma

&cat[[5*n, 12*n]: n in [1..27]];  // Bruno Berselli, Sep 30 2011

Mathematica

With[{nn=30},Riffle[5Range[nn],12Range[nn]]] (* or *) LinearRecurrence[ {0,2,0,-1},{5,12,10,24},60] (* Harvey P. Dale, Aug 18 2012 *)

PARI

a(n)=(n+1)\2*if(n%2,5,12) \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Bruno Berselli, Sep 30 2011: (Start)

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

a(n) = ((17+7*(-1)^n)/2)*((2*n-(-1)^n+1)/4) = (17*n+(7*n-5)*(-1)^n+5)/4.

a(n)*a(n+1) = a(10*s), where s is A002620(n+1).

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

Extensions

More terms from Bruno Berselli, Sep 30 2011