From: Living in the fair city of Melbourne, Australia
Well, I found the reference, for those interested.
FM 100-5, 1944 OPERATIONS
In Chapter 15, US formations are discussed, and here are a couple parts which might shed some light. On the topic of Infantry divisions organization, I found on page 297, paragraph #1011
1011. Three regiments of infantry and four battalions of Field Artillery comprise the major combat elements.[...]
which contrasts with the detailed description of and rationale about the organization of Armored Divisions, found on page 305, paragraph #1038:
1038. The armored division is organized for flexibility in the formation of combat teams. The self-contained battalion is the basic unit. The division consists of a headquarters, two combat commands, a reserve command, a cavalry mechanized reconnaissance squadron, three tank battalions, three infantry armored battalions, the division artillery consisting of a headquarters and three armored field artillery battalions, and armored engineer battalion, and signal and service troops. Units are attached to the two combat commands in the type and number desired for a particular operation.