OFFSET
0,2
COMMENTS
Size, in bytes, of a [9n]p widescreen resolution RGBA truecolor digital picture.
[9n]p pics are bitmap images with resolution of 16n X 9n pixels.
For example, in the case n = 80 we have a [9*80]p = 720p image where the resolution is 1280 X 720 pixels.
Colors are represented using 4 channels: red, green, blue, alpha (or transparency). In a truecolor image, a pixel uses 1 byte per channel, which means a total of 4 bytes per pixel.
Thus an image with a 16n X 9n resolution will take up 16n * 9n * 4 or (24n)^2 bytes of memory.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Wikipedia, 16:9 aspect ratio.
Wikipedia, Color depth.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = (24*n)^2 = 576*n^2 = 576 * A000290(n).
a(n) = 4*(16*n * 9*n).
From Colin Barker, Aug 14 2019: (Start)
G.f.: 576*x*(1 + x) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
E.g.f.: 576*exp(x)*x*(1 + x). - Stefano Spezia, Aug 14 2019
EXAMPLE
Digital pics with height 10 pixels and resolution 160 X 90 need a(10) = (24 * 10)^2 = 57600 bytes of memory to be stored.
720p HD images with resolution 1280 x 720 = (16 * 80) X (9 * 80) have size a(80) = (24 * 80)^2 = 3686400 bytes.
1080p FullHD images with resolution 1920 x 1080 = (16 * 120) X (9 * 120) have size a(120) = (24 * 120)^2 = 8294400 bytes.
MATHEMATICA
Table[(24 n)^2, {n, 0, 31}]
PROG
(PARI) concat(0, Vec(576*x*(1 + x) / (1 - x)^3 + O(x^40))) \\ Colin Barker, Aug 14 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Aug 13 2019
STATUS
approved