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 A213753 Rectangular array:  (row n) = b**c, where b(h) = 2*h-1, c(h) = -1 + 2^(n-1+h), n>=1, h>=1, and ** = convolution. 4
 1, 6, 3, 21, 16, 7, 58, 51, 36, 15, 141, 132, 111, 76, 31, 318, 307, 280, 231, 156, 63, 685, 672, 639, 576, 471, 316, 127, 1434, 1419, 1380, 1303, 1168, 951, 636, 255, 2949, 2932, 2887, 2796, 2631, 2352, 1911, 1276, 511, 5998, 5979, 5928, 5823 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Principal diagonal: A213754. Antidiagonal sums: A213755. Row 1,  (1,3,5,7,9,...)**(1,3,7,15,...): A047520. Row 2,  (1,3,5,7,9,...)**(3,7,15,31,...). Row 3,  (1,3,5,7,9,...)**(7,15,31,63...). Ror a guide to related arrays, see A213500. LINKS Clark Kimberling, Antidiagonals n = 1..60, flattened FORMULA T(n,k) = 5*T(n,k-1)-9*T(n,k-2)+7*T(n,k-3)-2*T(n,k-4). G.f. for row n:  f(x)/g(x), where f(x) = x*(-1 + 2^n + x + (-2 + 2^n)*x^2) and g(x) = (1 - 2*x)(1 - x )^3. EXAMPLE Northwest corner (the array is read by falling antidiagonals): 1....6.....21....58.....141 3....16....51....132....307 7....36....111...280....639 15...76....231...576....1303 31...156...471...1168...2631 MATHEMATICA b[n_] := 2 n - 1; 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}]  (* A213753 *) Table[t[n, n], {n, 1, 40}] (* A213754 *) s[n_] := Sum[t[i, n + 1 - i], {i, 1, n}] Table[s[n], {n, 1, 50}] (* A213755 *) CROSSREFS Cf. A213500. Sequence in context: A282217 A213756 A213551 * A213747 A286203 A286414 Adjacent sequences:  A213750 A213751 A213752 * A213754 A213755 A213756 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Jun 20 2012 STATUS approved

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Last modified April 23 01:52 EDT 2021. Contains 343198 sequences. (Running on oeis4.)