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Binomial transform of A100060.
0

%I #8 Nov 28 2017 11:35:44

%S 1,1,2,4,8,16,31,58,107,200,387,782,1640,3512,7542,16020,33406,68257,

%T 136971,271341,534302,1053441,2092840,4206655,8564397,17631551,

%U 36575711,76137143,158427407,328537434,677598776,1388303692,2824261172,5704560206,11443336382

%N Binomial transform of A100060.

%C 1 or 0 are assigned to increase or decrease in magnitude of a succession of terms in the first difference row of Zeta function heights, as recorded in A100060.

%F Use the binomial transform operation (bto) on A100060, i.e. (bto): [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1,

%e a(5) = 8 = 1*1 + 4*0 + 6*1 + 4*0 + 1*1.

%t nmax = 40; A100060 = (Sign[Differences[Im[ZetaZero[Range[nmax+2]]], 2]] + 1)/2; Flatten[{1, Table[1 + Sum[Binomial[n, k]*A100060[[k]], {k, 1, n}], {n, 1, nmax}]}] (* _Vaclav Kotesovec_, Nov 28 2017 *)

%Y Cf. A100060.

%K nonn

%O 1,3

%A _Gary W. Adamson_, May 01 2005

%E a(11) corrected by _Vaclav Kotesovec_, Nov 28 2017

%E More terms from _Vaclav Kotesovec_, Nov 28 2017