I have done an investigation of my own (on file ftp://ftp.ncbi.nih.gov/genomes/Homo_sapiens/CHR_20/hs_ref_GRCh38.p12_chr20.fa.gz).
Unless my method for calculating the frequencies is wrong or my script has a bug (quite likely actually), empirically at least, bases like to be next to some bases more than others, and the more they gather the more fussy they become. Almost a tenfold! Also note that this is for just 1 chromosome of HS. Maybe overall the differences even out which I don't believe.
AA => 0.0876441581694274,
AC => 0.050382172379123,
AG => 0.0726163599915327,
AT => 0.0680375702421899,
CA => 0.0744871531142771,
CC => 0.0586105336500266,
CG => 0.0121528607767549,
CT => 0.072435600501404,
GA => 0.0616385773891699,
GC => 0.0479870698325412,
GG => 0.0597908940638241,
GT => 0.0509971288041851,
TA => 0.0549250240353684,
TC => 0.0606918145805057,
TG => 0.0758458048289572,
TT => 0.0902412592104137,
AAA => 0.0335770294488858,
AAC => 0.0141652325290566,
AAG => 0.0191070631163639,
AAT => 0.0207919285470298,
ACA => 0.0195277849575718,
ACC => 0.0122296472539126,
ACG => 0.00301071191243409,
ACT => 0.015618504735689,
AGA => 0.0218989913762551,
AGC => 0.0155317569775754,
AGG => 0.0196529454780131,
AGT => 0.0155383292608308,
ATA => 0.016470891588768,
ATC => 0.0127097589265764,
ATG => 0.0175833302904619,
ATT => 0.0212709235696259,
CAA => 0.0176484150372629,
CAC => 0.0162805665608066,
CAG => 0.022908155898834,
CAT => 0.017649579543762,
CCA => 0.0198202675145805,
CCC => 0.0158003751274237,
CCG => 0.00344220145072305,
CCT => 0.0195463851572704,
CGA => 0.00252629316093788,
CGC => 0.00300099705684542,
CGG => 0.00358382458359042,
CGT => 0.00304285548223897,
CTA => 0.0116349353800189,
CTC => 0.01868181086631,
CTG => 0.0222707082316364,
CTT => 0.0198463333175886,
GAA => 0.0196784370038435,
GAC => 0.0100617509082632,
GAG => 0.0187920401801322,
GAT => 0.0131055794712754,
GCA => 0.0158572126158678,
GCC => 0.0139523511697284,
GCG => 0.00302848260065376,
GCT => 0.0151525107103092,
GGA => 0.0176044828331722,
GGC => 0.0139832983287465,
GGG => 0.0158069633628229,
GGT => 0.0123961876354327,
GTA => 0.0100987758340782,
GTC => 0.0100467877973565,
GTG => 0.0167909713545918,
GTT => 0.0140548755980838,
TAA => 0.0167405625801087,
TAC => 0.00987903505290584,
TAG => 0.0118104408663679,
TAT => 0.0164935276808539,
TCA => 0.0192795855518179,
TCC => 0.0166299982712662,
TCG => 0.00266904889601673,
TCT => 0.022118317401688,
TGA => 0.0195997929347923,
TGC => 0.015470963357463,
TGG => 0.0207474061136176,
TGT => 0.0200197809773843,
TTA => 0.0167229833176149,
TTC => 0.0192543333081449,
TTG => 0.019199106986227,
TTT => 0.035068794178565,
I will post the script I used shortly on the Meditations section as it may be of more general use.
