OFFSET
0,4
FORMULA
Conjecture: T(n, 1) = A329369(n).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
3, 5, 7, 9, 11, 13, 15, 17, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
7, 19, 37, 61, 91, 127, 169, 217, ...
3, 5, 7, 9, 11, 13, 15, 17, ...
7, 11, 15, 19, 23, 27, 31, 35, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
15, 65, 175, 369, 671, 1105, 1695, 2465, ...
PROG
(PARI) R(n, k)=my(L=logint(n, 2), A=n - 2^L); T(A, k)*k^(L - if(A>0, logint(A, 2) + 1) + 1)
T(n, k)=if(n==0, 1, R(n, k+1) - R(n, k))
(PARI) T(n, k) = my(A = 2*n+1, B, C, v1, v2); v1 = []; while(A > 0, B=valuation(A, 2); v1=concat(v1, B+1); A \= 2^(B+1)); v1 = Vecrev(v1); A = #v1; v2 = vector(A, i, 1); for(i=1, A-1, B = A-i; for(j=1, B, C = B-j+k+1; v2[j] = v2[j]*C^v1[B] - v2[j+1]*(C-1)^v1[B])); v2[1] \\ Mikhail Kurkov, Apr 30 2024
CROSSREFS
KEYWORD
AUTHOR
Mikhail Kurkov, Nov 20 2022
STATUS
approved