A147789 a(n) = round(2*(3/2)^n), using round-to-even method.

3, 4, 7, 10, 15, 23, 34, 51, 77, 115, 173, 259, 389, 584, 876, 1314, 1971, 2956, 4434, 6651, 9976, 14964, 22445, 33668, 50502, 75754, 113630, 170445, 255668, 383502, 575253, 862880, 1294320, 1941479, 2912219, 4368329, 6552493, 9828740, 14743110

Offset

1,1

Comments

See Wikipedia link and MathWorld link for different methods of rounding half-integers.

Different from recursion a(1) = 3, a(n) = round(a(n-1)*3/2) for n > 1, which gives a(2) = 4, a(3) = 6, a(4) = 9, a(5) = 14, ... (see A147790).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Nearest Integer Function

Wikipedia, Rounding

Example

a(4) = round(2*(3/2)^4) = round(81/8) = round(10 + 1/8) = 10.

Mathematica

Round[2(3/2)^Range[40]] (* Harvey P. Dale, Feb 04 2012 *)

Prog

(Magma) RoundToEven:=function(n); d:=Floor(n); if n-d ne 1/2 then return Round(n); else return d+(d mod 2); end if; end function; [ RoundToEven(2*(3/2)^n):n in [1..39] ]; // Klaus Brockhaus, Nov 17 2008
(PARI) {RoundToEven(n)=local(d); d=divrem(n, 1); if(d[2]<>1/2, round(n), d[1]+d[1]%2)}
{for(n=1, 39, print1(RoundToEven(2*(3/2)^n), ", "))} \\ Klaus Brockhaus, Nov 17 2008

Crossrefs

Cf. A061418, A147788, A147790.

Sequence in context: A105343 A237834 A147955 * A047625 A147871 A368896

Adjacent sequences: A147786 A147787 A147788 * A147790 A147791 A147792

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Nov 13 2008

Extensions

Edited by Klaus Brockhaus, Nov 17 2008

Status

approved