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 A339282 Triangle read by rows: T(n,k) is the number of unoriented series-parallel networks with n colored elements using exactly k colors. 6
 1, 2, 2, 4, 14, 10, 11, 84, 168, 98, 30, 522, 2109, 3004, 1396, 98, 3426, 24397, 63094, 67660, 25652, 328, 23404, 274626, 1142420, 2119985, 1805082, 576010, 1193, 165417, 3065376, 19230320, 54916745, 78809079, 55503392, 15282038, 4459, 1197934, 34201068, 311157620, 1283360335, 2761083930, 3220245007, 1932118328, 467747416 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Unoriented version of A339228. Equivalence is up to reversal of all parts combined in series. LINKS Table of n, a(n) for n=1..45. EXAMPLE Triangle begins: 1; 2, 2; 4, 14, 10; 11, 84, 168, 98; 30, 522, 2109, 3004, 1396; 98, 3426, 24397, 63094, 67660, 25652; 328, 23404, 274626, 1142420, 2119985, 1805082, 576010; ... PROG (PARI) \\ R(n, k) gives colorings using at most k colors as a vector. EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} B(n, Z)={my(p=Z+O(x^2)); for(n=2, n, p=x*Ser(EulerT(Vec(p^2/(1+p)+Z)))); p} R(n, k)={my(Z=k*x, q=subst(B((n+1)\2, Z), x, x^2), s=subst(Z, x, x^2)+q^2/(1+q), p=Z+O(x^2), t=p); for(n=1, n\2, t=Z + q*(1 + p); p=Z + x*Ser(EulerT(Vec(t+(s-subst(t, x, x^2))/2))) - t); Vec(p+t-Z+B(n, Z))/2} M(n)={my(v=vector(n, k, R(n, k)~)); Mat(vector(n, k, sum(i=1, k, (-1)^(k-i)*binomial(k, i)*v[i])))} {my(T=M(8)); for(n=1, #T~, print(T[n, 1..n]))} CROSSREFS Columns 1..2 are A339225, A339281. Row sums are A339283. Cf. A339228, A339280, A339285. Sequence in context: A120654 A121514 A121526 * A153956 A153962 A261980 Adjacent sequences: A339279 A339280 A339281 * A339283 A339284 A339285 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Nov 30 2020 STATUS approved

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Last modified June 19 09:20 EDT 2024. Contains 373494 sequences. (Running on oeis4.)