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Main diagonal of array in A038150.
1

%I #22 Nov 04 2023 17:49:40

%S 1,6,29,97,343,1131,3338,10336,29644,88555,260497,728358,2103284,

%T 6020698,16594432,46969365,128670281,361020986,1008411198,2742388946,

%U 7613161908,20632925370,56988914979,156977658446,423559114311

%N Main diagonal of array in A038150.

%H A. S. Fraenkel, <a href="https://doi.org/10.1016/S0304-3975(00)00062-1">Recent results and questions in combinatorial game complexities</a>, Theoretical Computer Science, vol. 249, no. 2 (2000), 265-288.

%H A. S. Fraenkel, <a href="https://doi.org/10.1016/S0304-3975(01)00070-6">Arrays, numeration systems and Frankenstein games</a>, Theoret. Comput. Sci. 282 (2002), 271-284; <a href="http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/ans1.ps">preprint</a>.

%F a(n) = F(2n)*n + F(2n+1)*A026351(n). - _Charlie Neder_, Feb 07 2019

%t max = 24; t[0, 0] = 1; t[n_, 1] := t[n, 1] = 2*t[n, 0]+n+1; t[n_, 0] := t[n, 0] = Catch[For[ u = Table[t[m, k], {m, 0, n-1}, {k, 0, max - m}] // Flatten // Union; k = 1, k <= n*(n+1)/2+1 , k++, If[u[[k]] != k, Throw[k]]]]; t[n_, k_] := t[n, k] = 3*t[n, k-1] - t[n, k-2] ; a[n_] := t[n, n]; Table[a[n], {n, 0, max}] (* _Jean-François Alcover_, Jan 02 2013 *)

%Y Cf. A026351, A038150.

%K nonn,nice,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Naohiro Nomoto_, Jun 07 2001