A132727 a(n) = 3 * 2^(n-1) * a(n-1) with a(0) = 1.

1, 3, 18, 216, 5184, 248832, 23887872, 4586471424, 1761205026816, 1352605460594688, 2077601987473440768, 6382393305518410039296, 39213424469105111281434624, 481854559876363607426268659712

Offset: 0

Author

Roger L. Bagula, Nov 17 2007

Keywords

• nonn

Comments

Power sequence relate to the Pythagorean musical scale: v(n,m) = v[0] * (3 * 2^n * m) starting at m = 1: a(n) = 3 * 2^(n-1) * a(n-1).

Hankel transform of A089022 with interpolated zeros. - Paul Barry, Mar 17 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 0..80

Programs

Magma

[3^n*2^Binomial(n, 2): n in [0..20]]; // G. C. Greubel, Feb 14 2021

Mathematica

a[n_]:= a[n]= If[n<2, 2^(n+1) -1, 3*2^(n-1)*a[n-1]]; Table[a[n], {n, 0, 20}]

Sage

[3^n*2^binomial(n, 2) for n in (0..20)] # G. C. Greubel, Feb 14 2021

Formula

a(n) = 3^n * 2^binomial(n,2). - Paul Barry, Mar 17 2008

Extensions

Offset changed by G. C. Greubel, Feb 14 2021