Revision History for A301922
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#15 by Alois P. Heinz at Wed Aug 21 05:32:28 EDT 2019
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#14 by Alois P. Heinz at Wed Aug 21 05:19:57 EDT 2019
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| FORMULA
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T(n,k) = A309858(n,k) - A309858(n-1,k). - Alois P. Heinz, Aug 21 2019
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| CROSSREFS
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Cf. A003465, A055621, A298422, A298426, A299471, A301481, A301920, A306017-A306021, A309858.
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#13 by Alois P. Heinz at Wed Aug 21 05:16:22 EDT 2019
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| MAPLE
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g:= (l, i, n)-> `if`(i=0, `if`(n=0, [[]], []), [seq(map(x->
[x[], j], g(l, i-1, n-j))[], j=0..min(l[i], n))]):
h:= (p, v)-> (q-> add((s-> add(`if`(andmap(i-> irem(k[i], p[i]
/igcd(t, p[i]))=0, [$1..q]), mul((m-> binomial(m, k[i]*m
/p[i]))(igcd(t, p[i])), i=1..q), 0), t=1..s)/s)(ilcm(seq(
`if`(k[i]=0, 1, p[i]), i=1..q))), k=g(p, q, v)))(nops(p)):
b:= (n, i, l, v)-> `if`(n=0 or i=1, 2^((p-> h(p, v))([l[], 1$n]))
/n!, add(b(n-i*j, i-1, [l[], i$j], v)/j!/i^j, j=0..n/i)):
A:= proc(n, k) A(n, k):= `if`(k>n-k, A(n, n-k), b(n$2, [], k)) end:
T:= (n, k)-> A(n, k)-A(n-1, k):
seq(seq(T(n, k), k=1..n), n=1..9); # Alois P. Heinz, Aug 21 2019
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| STATUS
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approved
editing
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#12 by N. J. A. Sloane at Sat Aug 10 17:38:44 EDT 2019
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#11 by Andrew Howroyd at Sat Aug 10 13:10:25 EDT 2019
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#10 by Andrew Howroyd at Sat Aug 10 11:13:41 EDT 2019
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| PROG
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(PARI)
permcount(v)={my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
rep(typ)={my(L=List(), k=0); for(i=1, #typ, k+=typ[i]; listput(L, k); while(#L<k, listput(L, #L))); Vec(L)}
can(v, f)={my(d=1, u=v); while(d>0, u=vecsort(apply(f, u)); d=lex(u, v)); !d}
Q(n, k, perm)={my(t=0); forsubset([n, k], v, t += can(Vec(v), t->perm[t])); t}
U(n, k)={my(s=0); forpart(p=n, s += permcount(p)*2^Q(n, k, rep(p))); s/n!}
for(n=1, 10, for(k=1, n, print1(U(n, k)-U(n-1, k), ", ")); print) \\ Andrew Howroyd, Aug 10 2019
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#9 by Andrew Howroyd at Fri Aug 09 22:28:46 EDT 2019
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| DATA
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1, 1, 1, 1, 2, 1, 1, 7, 3, 1, 1, 23, 29, 4, 1, 1, 122, 2102, 150, 5, 1, 1, 888, 7011184, 7013164, 1037, 6, 1, 1, 11302, 1788775603336, 29281354507753848, 1788782615612, 12338, 7, 1, 1, 262322, 53304526022885280592, 234431745534048893449761040648512, 234431745534048922729326772799024, 53304527811667884902, 274659, 8, 1
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| LINKS
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Andrew Howroyd, <a href="/A301922/b301922.txt">Table of n, a(n) for n = 1..91</a>
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| KEYWORD
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nonn,tabl,more
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| EXTENSIONS
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Terms a(16) and beyond from Andrew Howroyd, Aug 09 2019
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| STATUS
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approved
editing
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#8 by Susanna Cuyler at Tue Jun 19 22:13:37 EDT 2018
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#7 by Gus Wiseman at Tue Jun 19 21:51:07 EDT 2018
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#6 by Gus Wiseman at Tue Jun 19 21:50:54 EDT 2018
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| KEYWORD
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nonn,tabl,changed,more
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