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%I #32 May 26 2024 08:21:12
%S 1,1,2,1,3,1,3,3,2,5,1,7,1,6,1,6,3,5,5,2,4,1,7,4,2,9,1,11,1,6,5,4,5,4,
%T 3,7,3,9,5,6,7,7,7,5,9,6,5,7,5,5,8,1,11,6,7,7,9,10,1,9,9,6,9,6,11,7,
%U 13,1,12,1,14,1,16,1,17,1,19,1,14,7,9,7,11
%N a(n) is the length of the longest palindromic subsequence at symmetrically-spaced indices ending at a(n-1); a(1)=1.
%C A set of indices is symmetric if, listed in increasing or decreasing order, its first differences are a palindromic sequence.
%C A new value is always followed by 1.
%C An alternate definition: a(n) is the largest number of coincidences between the subsequence enclosed by m..n-1 and its reverse, where a(n-1)=a(m), maximized over m.
%H Neal Gersh Tolunsky, <a href="/A368290/b368290.txt">Table of n, a(n) for n = 1..10000</a>
%H Neal Gersh Tolunsky, <a href="/A368290/a368290.png">Ordinal transform of first 30000 terms</a>.
%H Neal Gersh Tolunsky, <a href="/A368290/a368290_1.png">Graph of first 100000 terms</a>.
%e a(10)=5 because we find the following length-5 palindromic subsequence at symmetric indices ending at i=a(n-1)=a(9)=2:
%e S: 1,1,2,1,3,1,3,3,2
%e P: 2, 3,1,3, 2
%e a(14)=6 because of the following length-6 palindromic subsequence:
%e S: 1,1,2,1,3,1,3,3,2,5,1,7,1
%e P: 1, 1, 3,3, 1, 1
%o (PARI) { for (n = 1, #a = vector(83, n, 1), for (k = 1, n-1, if (a[k] == a[n-1], a[n] = max(a[n], sum (i = k, n-1, a[i] == a[n-1+k-i]);););); print1 (a[n]", ");); } \\ _Rémy Sigrist_, Dec 20 2023
%Y Cf. A308659, A362881.
%K nonn
%O 1,3
%A _Neal Gersh Tolunsky_, Dec 19 2023
%E More terms from _Rémy Sigrist_, Dec 20 2023
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