Difference between revisions of "OEIS/Coordination sequences for lattices"
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< OEIS
(Created page with "The recurrences were derived by Mathematica: bin[n_,k_]:=(n!/(nk)!/k!); === C_n === * [https://oeis.org/A103884 A103884 (C_4)] d:= 4; CoefficientList[Series[(Sum[Binomial[...") 
(No difference)

Revision as of 15:50, 28 July 2020
The recurrences were derived by Mathematica:
bin[n_,k_]:=(n!/(nk)!/k!);
C_n
d:= 4; CoefficientList[Series[(Sum[Binomial[2n,2k]*x^k, {k, 0, d}])/(1x)^d, {x,0,11}],x] {1, 32, 192, 608, 1408, 2720, 4672, 7392, 11008, 15648, 21440, 28512} InputForm[FullSimplify[bin[2*n,2*k]/bin[2*n,2*k2]]] > ((1 + 2*k  2*n)*(1 + k  n))/(k*(1 + 2*k)) n:=4; f:= gfun:rectoproc({a(k)=(2*n2*k+1)*(n(k1))/(k*(2*k1))*a(k1),a(0)=1},a(k),remember): map(f, [$0 Recurrence: a(k)=(2*n2*k+1)*(n(k1))/(k*(2*k1))*a(k1), a(0)=1, k=0..n