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 A213590 Rectangular array:  (row n) = b**c, where b(h) = h^2, c(h) = F(n-1+h), F = A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution. 6
 1, 5, 1, 15, 6, 2, 36, 20, 11, 3, 76, 51, 35, 17, 5, 148, 112, 87, 55, 28, 8, 273, 224, 188, 138, 90, 45, 13, 485, 421, 372, 300, 225, 145, 73, 21, 839, 758, 694, 596, 488, 363, 235, 118, 34, 1424, 1324, 1243, 1115, 968, 788, 588, 380, 191, 55, 2384 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Principal diagonal: A213504. Antidiagonal sums: A213557. Row 1,  (1,4,9,16,...)**(1,1,2,3,5,...): A053808. Row 2,  (1,4,9,16,...)**(1,2,3,5,8,...). Row 3,  (1,4,9,16,...)**(2,3,5,8,13,...). For a guide to related arrays, see A213500. LINKS Clark Kimberling, Antidiagonals n = 1..60, flattened FORMULA Rows:  T(n,k) = 4*T(n,k-1)-5*T(n,k-2)+*T(n,k-3)+2*T(n,k-4)-T(n,k-5). Columns:  T(n,k)=T(n-1,k) + T(n-2,k). G.f. for row n:  f(x)/g(x), where f(x) = F(n) + F(n+1)*x + F(n-1)*x^2 and g(x) = (1 - x - x^2)*(1 - x )^3. EXAMPLE Northwest corner (the array is read by falling antidiagonals): 1....5....15....36....76.....148 1....6....20....51....112....224 2....11...35....87....188....372 3....17...55....138...300....596 5....28...90....225...488....868 8....45...145...363...788....1564 13...73...235...588...1276...2532 MATHEMATICA b[n_] := n^2; c[n_] := Fibonacci[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}]  (* A213590 *) Table[t[n, n], {n, 1, 40}] (* A213504 *) s[n_] := Sum[t[i, n + 1 - i], {i, 1, n}] Table[s[n], {n, 1, 50}] (* A213557 *) CROSSREFS Cf. A213500, A213587. Sequence in context: A295574 A087727 A039807 * A185263 A264616 A157395 Adjacent sequences:  A213587 A213588 A213589 * A213591 A213592 A213593 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Jun 19 2012 STATUS approved

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Last modified October 22 15:45 EDT 2018. Contains 316490 sequences. (Running on oeis4.)