proposed

approved

editing

proposed

The round (nearest) function uses the convention that values half-way halfway between two integers are rounded up, so a(4) = 37 = round(36 + 1/2).

The central unit square has perimeter 4. At n=1, the additional 4 squares hide 4*1/2 = 2 units of length and add 4*3*1/2 = 6 units, to give a(1) = 4 - 2 + 6 = 8.

At n=2, the additional 12 squares hide 12*1/(2*2) units of length and add 12*3*1/(2*2) to give a(2) = 8 - 12/4 + 36/4 = 14.

Cf. A083313.

approved

editing

reviewed

approved

proposed

reviewed

editing

proposed

The central unit square has perimeter 4. At n=1, the additional 4 squares hide 4*1/2=2 units of length and add 4*3*1/2=6 units, to give a(1) = 4-2+6 = 8.

At n=2, the additional 12 squares hide 12*1/(2*2) units of length and add 12*3*1/(2*2) to give a(2)=8-12/4+36/4=14.

A227621 := proc(n)

if n = 0 then 4

else

round(A083313(n)/2^(n-3)) ;

end if;

end proc: # R. J. Mathar, Aug 01 2013

4, 18, 8, 14, 23, 36, 37, 57, 87, 133, 201, 304, 457, 688, 1034, 1553, 2331, 3499, 5251, 7878, 11819, 17731, 26598, 39899, 59851, 89778, 134669, 202005, 303010, 454517, 681778, 1022668, 1534004, 2301009, 3451515, 5177275, 7765914

The round (nearest) function uses the convention that values half-way between two integers are rounded up, so a(4) = 37 = round(36 +1/2).

proposed

editing

editing

proposed

4, 18, 14, 23, 37, 36, 57, 87, 133, 201, 304, 457, 688, 1034, 1553, 2331, 3499, 5251, 7878, 11819, 17731, 26598, 39899, 59851, 89778, 134669, 202005, 303010, 454517, 681778, 1022668, 1534004, 2301009, 3451515, 5177275

a(n) = round(x(n)); x(0) = 4, ; for n >= 1, xa(n) = x(n-1)+ 8*round(3^A083313(n-1)/2^(n-3)).

(Small Basic)

a[0]=4

For n = 0 To 51

a[n+1] = Math.Round((Math.Power(3, n+1) - Math.Power(2, n))/Math.Power(2, n-2))

TextWindow.Write(a[n]+", ")

EndFor

Cf. A083313