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 A202873 Symmetric matrix based on (1,3,7,15,31,...), by antidiagonals. 3
 1, 3, 3, 7, 10, 7, 15, 24, 24, 15, 31, 52, 59, 52, 31, 63, 108, 129, 129, 108, 63, 127, 220, 269, 284, 269, 220, 127, 255, 444, 549, 594, 594, 549, 444, 255, 511, 892, 1109, 1214, 1245, 1214, 1109, 892, 511, 1023, 1788, 2229, 2454, 2547, 2547, 2454 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let s=(1,3,7,15,31,...) and let T be the infinite square matrix whose n-th row is formed by putting n-1 zeros before the terms of s.  Let T' be the transpose of T.  Then A202873 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A202767 for characteristic polynomials of principal submatrices of M. LINKS EXAMPLE Northwest corner: 1.....3.....7...15...31.....63 3....10....24...52...108...220 7....24....59..129...269...549 15...52...129..284...594..1214 31...108..269..594..1245..2547 MATHEMATICA s[k_] := -1 + 2^k; U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[s[k], {k, 1, 15}]]; L = Transpose[U]; M = L.U; TableForm[M] m[i_, j_] := M[[i]][[j]]; Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]] f[n_] := Sum[m[i, n], {i, 1, n}] + Sum[m[n, j], {j, 1, n - 1}] Table[f[n], {n, 1, 12}] Table[Sqrt[f[n]], {n, 1, 12}] (* A000295, Eulerian *) Table[m[1, j], {j, 1, 12}]    (* A000225 *) Table[m[2, j], {j, 1, 12}]    (* A053208 *) CROSSREFS Cf. A202767. Sequence in context: A117525 A075149 A161618 * A157933 A013915 A136445 Adjacent sequences:  A202870 A202871 A202872 * A202874 A202875 A202876 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 26 2011 STATUS approved

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Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)