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 A284877 Irregular triangle T(n,k) for 1 <= k <= n/2 + 1: T(n,k) = number of double palindrome structures of length n using exactly k different symbols. 7
 1, 1, 1, 1, 3, 1, 7, 2, 1, 15, 5, 1, 25, 21, 3, 1, 49, 42, 7, 1, 79, 122, 44, 4, 1, 129, 225, 90, 9, 1, 211, 570, 375, 80, 5, 1, 341, 990, 715, 165, 11, 1, 517, 2321, 2487, 930, 132, 6, 1, 819, 3913, 4550, 1820, 273, 13, 1, 1275, 8827, 14350, 8330, 2009, 203, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A double palindrome is the concatenation of two palindromes. Permuting the symbols will not change the structure. For the purposed of this sequence, valid palindromes include both the empty word and a singleton symbol. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..960 FORMULA T(n, k) = (Sum_{j=0..k} (-1)^j * binomial(k, j) * A284873(n, k-j)) / k!. T(n, k) = r(n, k) - Sum_{d|n, d 1 n = 2: aa; ab => 1 + 1 n = 3: aaa; aab, aba, abb => 1 + 3 n = 4: aaaa; aaab, aaba, aabb, abaa, abab, abba, abbb; abac, abcb => 1 + 7 + 2 MATHEMATICA r[d_, k_]:=If[OddQ[d], d*k^((d + 1)/2), (d/2)*(k + 1)*k^(d/2)]; a[n_, k_]:= r[n, k] - Sum[If[d

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)