A265080 Array read by antidiagonals, arising from study of remixing keys in public-key cryptography.
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 4, 12, 18, 4, 0, 0, 5, 20, 51, 44, 5, 0, 0, 6, 30, 108, 192, 110, 6, 0, 0, 7, 42, 195, 544, 675, 252, 7, 0, 0, 8, 56, 318, 1220, 2540, 2358, 588, 8, 0, 0, 9, 72, 483, 2364, 7145, 11544, 8043, 1304, 9, 0
Offset: 0
Examples
Array begins: 0, 0, 0, 0, 0, 0, ... 0, 1, 2, 3, 4, 5, ... 0, 2, 6, 12, 20, 30, ... 0, 3, 18, 51, 108, 195, ... 0, 4, 44, 192, 544, 1220, ... 0, 5, 110, 675, 2540, 7145, ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)
- Daniel R. L. Brown, Bounds on surmising remixed keys, IACR, Report 2015/375, 2015-2016. See Table 1.
Crossrefs
Programs
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PARI
Q(p)={my(S=Set(p));prod(i=1, #S, (#select(t->t==S[i],p))!)} T(n,k)={my(s=0); if(n, forpart(p=n, s+=p[#p]*n!*(#p)!*binomial(k,#p) / (prod(i=1,#p,p[i]!) * Q(Vec(p))))); s} \\ Andrew Howroyd, Mar 20 2021 -
PARI
T(n,k) = {n!*polcoef(sum(j=0, n, exp(x + O(x*x^n))^k - sum(i=0, j, x^i/i!, O(x*x^n))^k), n)} \\ Andrew Howroyd, Aug 09 2025
Formula
T(n,k) = n! * [x^n] Sum_{j>=0} (exp(x)^k - (Sum_{i=0..j} x^i/i!)^k). - Andrew Howroyd, Aug 09 2025
Extensions
More terms from Henry Bottomley, Mar 20 2021
Comments