A186340 a(n) = 2^A001840(n).

1, 2, 4, 8, 32, 128, 512, 4096, 32768, 262144, 4194304, 67108864, 1073741824, 34359738368, 1099511627776, 35184372088832, 2251799813685248, 144115188075855872, 9223372036854775808, 1180591620717411303424, 151115727451828646838272

Offset

0,2

Comments

A factor in the Hankel transform A186339 of A186338.

a(n)*a(n-4) = 2*a(n-1)*a(n-3) = a(n-1)*a(n-3) + c(n)*a(n-2)^2, where c(3*n+2) = 2, c(3*n) = c(3*n+1) = 1 for all n in Z. - Michael Somos, Oct 19 2018

Links

Table of n, a(n) for n=0..20.

Formula

a(n)=2^floor((n+1)(n+2)/6).

Example

G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 32*x^4 + 128*x^5 + 512*x^6 + ... - Michael Somos, Oct 19 2018

Mathematica

a[ n_] := 2^Quotient[ Binomial[n + 2, 2], 3]; (* Michael Somos, Oct 19 2018 *)

Prog

(PARI) {a(n) = 2^(binomial(n+2, 2)\3)}; /* Michael Somos, Oct 19 2018 */

Crossrefs

Cf. A058937.

Sequence in context: A192008 A298989 A074406 * A228920 A064378 A191650

Adjacent sequences: A186337 A186338 A186339 * A186341 A186342 A186343

Keyword

nonn,easy

Author

Paul Barry, Feb 18 2011

Status

approved