A329495
Numerator of second moment of the n-th term of Ulam's "history-dependent random sequence".
Original entry on oeis.org
1, 4, 25, 101, 655, 11077, 94199, 2005319, 62541113, 530615357, 3888615949, 2547768661, 1603125774433, 510235838011, 76538488318091, 10462945272539099, 182249306891497151, 7488308007918913129, 6810487755999748187
Offset: 1
1, 4, 25/2, 101/3, 655/8, 11077/60, 94199/240, 2005319/2520, ...
-
s:=[1]; a:=[0];
for N from 2 to 40 do # N = n+1
n:=N-1;
t1:=s[n]+(1/n)*add(s[k],k=1..n)+2*s[n]/n+(2/n)*a[n];
t2:=s[n]+(1/n)*add(s[k],k=1..n)+a[n]+(2/n)*add(a[k],k=1..n);
s:=[op(s),t1];
a:=[op(a),t2];
od:
s; # sigma_n
a; # alpha_n
sn:=map(numer,s); # A329495
sd:=map(denom,s); # A329496
an:=map(numer,a); # A329497
ad:=map(denom,a); # A329498
A329496
Denominator of second moment of the n-th term of Ulam's "history-dependent random sequence".
Original entry on oeis.org
1, 1, 2, 3, 8, 60, 240, 2520, 40320, 181440, 725760, 266112, 95800320, 17791488, 1585059840, 130767436800, 1394852659200, 35568742809600, 20324995891200, 12164510040883200, 69511485947904000, 5109094217170944000, 32114306507931648000
Offset: 1
1, 4, 25/2, 101/3, 655/8, 11077/60, 94199/240, 2005319/2520, ...
-
s:=[1]; a:=[0];
for N from 2 to 40 do # N = n+1
n:=N-1;
t1:=s[n]+(1/n)*add(s[k],k=1..n)+2*s[n]/n+(2/n)*a[n];
t2:=s[n]+(1/n)*add(s[k],k=1..n)+a[n]+(2/n)*add(a[k],k=1..n);
s:=[op(s),t1];
a:=[op(a),t2];
od:
s; # sigma_n
a; # alpha_n
sn:=map(numer,s); # A329495
sd:=map(denom,s); # A329496
an:=map(numer,a); # A329497
ad:=map(denom,a); # A329498
A329498
Denominator of the rational number alpha_n involved in the calculation of the second moment of the n-th term of Ulam's "history-dependent random sequence".
Original entry on oeis.org
1, 1, 2, 6, 24, 120, 720, 1680, 40320, 362880, 725760, 7983360, 2128896, 113218560, 387459072, 261534873600, 836911595520, 71137485619200, 75322043596800, 1621934672117760, 37429261664256000, 10218188434341888000, 224800145555521536000
Offset: 1
0, 2, 21/2, 223/6, 2603/24, 33623/120, 477977/720, 2474153/1680, ...
-
s:=[1]; a:=[0];
for N from 2 to 40 do # N = n+1
n:=N-1;
t1:=s[n]+(1/n)*add(s[k],k=1..n)+2*s[n]/n+(2/n)*a[n];
t2:=s[n]+(1/n)*add(s[k],k=1..n)+a[n]+(2/n)*add(a[k],k=1..n);
s:=[op(s),t1];
a:=[op(a),t2];
od:
s; # sigma_n
a; # alpha_n
sn:=map(numer,s); # A329495
sd:=map(denom,s); # A329496
an:=map(numer,a); # A329497
ad:=map(denom,a); # A329498
Showing 1-3 of 3 results.