This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Triangle begins:
k = 1 2 3 4 5
n= 2: 4;
n= 3: 8, 1;
n= 4: 16, 1;
n= 5: 32, 0, 2;
n= 6: 64, 6;
n= 7: 128, 8;
n= 8: 256, 16, 4;
n= 9: 512, 26;
n=10: 1024, 17, 10;
n=11: 2048, 67, 4, 3;
n=12: 4096, 100, 10;
n=13: 8192, 137, 34, 6;
n=14: 16384, 426, 28, 1;
n=15: 32768, 661, 96, 6;
n=16: 65536, 1351, 146, 16, 8;
n=17: 131072, 2637, 230, 15;
n=18: 262144, 3831, 258, 40;
n=19: 524288, 8095, 1130, 50;
n=20: 1048576, 15241, 854, 77, 6;
...
The T(6,2) = 6 solutions are:
- 1^2 - 2^2 + 3^2 - 4^2 + 5^2 + 6^2 = 49 = 7^2,
- 1^2 - 2^2 + 3^2 + 4^2 + 5^2 - 6^2 = 9 = 3^2,
- 1^2 - 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 81 = 9^2,
+ 1^2 - 2^2 + 3^2 - 4^2 - 5^2 + 6^2 = 1 = 1^2,
+ 1^2 + 2^2 - 3^2 + 4^2 + 5^2 - 6^2 = 1 = 1^2,
+ 1^2 + 2^2 + 3^2 - 4^2 - 5^2 + 6^2 = 9 = 3^2.
f(k,u)=my(x=0,v=vector(#u));for(i=1,#u,u[i]=if(u[i]==0,-1,1);v[i]=i^k);u*v~ is(k,u)=my(x=f(k,u));ispower(x,k) T(n,k)=my(u=vector(n,i,[0,1]),nbsol=0);if(k%2==1,u[1]=[1,1]);forvec(X=u,if(is(k,X),nbsol++));if(k%2==1,nbsol*=2);nbsol
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