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 A213747 Rectangular array:  (row n) = b**c, where b(h) = -1 + 2^h, c(h) = b(n-1+h), n>=1, h>=1, and ** = convolution. 4
 1, 6, 3, 23, 16, 7, 72, 57, 36, 15, 201, 170, 125, 76, 31, 522, 459, 366, 261, 156, 63, 1291, 1164, 975, 758, 533, 316, 127, 3084, 2829, 2448, 2007, 1542, 1077, 636, 255, 7181, 6670, 5905, 5016, 4071, 3110, 2165, 1276, 511, 16398, 15375, 13842 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Principal diagonal: A213748. Antidiagonal sums: A213749. Row 1,  (1,3,7,15,31,...)**(1,3,7,15,31,...): A045618. Row 2,  (1,3,7,15,31,...)**(3,7,15,31,...). Row 3,  (1,3,7,15,31,...)**(7,15,31,...). For a guide to related arrays, see A213500. LINKS Clark Kimberling, Antidiagonals n = 1..60, flattened FORMULA T(n,k) = 6*T(n,k-1)-13*T(n,k-2)+12*T(n,k-3)-4*T(n,k-4). G.f. for row n:  f(x)/g(x), where f(x) = -1 + 2^n - (-2 - 2^n)*x and g(x) = (1 - 3*x + 2*x^2 )^2. EXAMPLE Northwest corner (the array is read by falling antidiagonals): 1....6.....23....72.....201 3....16....57....170....459 7....36....125...366....975 15...76....261...758....1007 31...156...533...1542...4071 MATHEMATICA b[n_] := -1 + 2^n; c[n_] := -1 + 2^n; t[n_, k_] := Sum[b[k - i] c[n + i], {i, 0, k - 1}] TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]] Flatten[Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}]] r[n_] := Table[t[n, k], {k, 1, 60}]  (* A213747 *) Table[t[n, n], {n, 1, 40}] (* A213748 *) s[n_] := Sum[t[i, n + 1 - i], {i, 1, n}] Table[s[n], {n, 1, 50}] (* A213749 *) CROSSREFS Cf. A213500. Sequence in context: A213756 A213551 A213753 * A286203 A286414 A288331 Adjacent sequences:  A213744 A213745 A213746 * A213748 A213749 A213750 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Jun 19 2012 STATUS approved

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Last modified April 5 20:24 EDT 2020. Contains 333260 sequences. (Running on oeis4.)