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 A262742 Irregular table read by rows: T(n,k) is the number of binary symmetric n X n matrices with exactly k 1's; n>=0, 0<=k<=n^2. Where the symmetry axes are in horizontal and vertical. 2
 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1, 1, 1, 4, 4, 10, 10, 20, 20, 31, 31, 40, 40, 44, 44, 40, 40, 31, 31, 20, 20, 10, 10, 4, 4, 1, 1, 1, 0, 0, 0, 9, 0, 0, 0, 36, 0, 0, 0, 84, 0, 0, 0, 126, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS The row length of this irregular triangle is n^2+1 = A002522(n). Inspired by A262666, but rotating the diagonal and antidiagonal symmetry axis to horizontal and vertical axes. From Wolfdieter Lang, Oct 12 2015 (Start): Double symmetry of n X n matrix M: M(i, j) = M(n-i+1, j) = M(i, n-j+1) (= M(n-i+1, n-j+1)), here with entries from {0, 1}. Due to 0 <-> 1 flip the rows are symmetric. The number of independent entries in such an n X n doubly symmetric matrix is A008794(n+1) (squares repeated). Therefore, the row sums give repeated A002416 (omitting the first 1): 1, 2, 2, 16, 16, 512, 512, ... (End) - Wolfdieter Lang, Oct 12 2015 LINKS Table of n, a(n) for n=0..79. Kival Ngaokrajang, Illustration of initial terms EXAMPLE Irregular table begins: n\k 0 1 2 3 4 5 6 7 8 9 ... 0: 1 1: 1 1 2: 1 0 0 0 1 3: 1 1 2 2 2 2 2 2 1 1 ... Row 4: 1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1; Row 5: 1, 1, 4, 4, 10, 10, 20, 20, 31, 31, 40, 40, 44, 44, 40, 40, 31, 31, 20, 20, 10, 10, 4, 4, 1, 1. ... CROSSREFS Cf. A262666,A002522, A008794, A002416. Sequence in context: A340172 A163529 A283655 * A360078 A027354 A192227 Adjacent sequences: A262739 A262740 A262741 * A262743 A262744 A262745 KEYWORD nonn,tabf AUTHOR Kival Ngaokrajang, Sep 29 2015 EXTENSIONS More terms from Alois P. Heinz, Sep 29 2015 STATUS approved

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Last modified September 7 23:15 EDT 2024. Contains 375749 sequences. (Running on oeis4.)