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 A294453 Array read by antidiagonals: T(0,k) = A000045(k+1) for k >= 0. T(n,0) = 1 for n >= 0; thereafter T(n,k) = T(n-1,k-1)+T(n-1,k) for n, k >= 1. 1
 1, 1, 1, 1, 2, 2, 1, 3, 3, 3, 1, 4, 5, 5, 5, 1, 5, 8, 8, 8, 8, 1, 6, 12, 13, 13, 13, 13, 1, 7, 17, 21, 21, 21, 21, 21, 1, 8, 23, 33, 34, 34, 34, 34, 34, 1, 9, 30, 50, 55, 55, 55, 55, 55, 55, 1, 10, 38, 73, 88, 89, 89, 89, 89, 89, 89, 1, 11, 47, 103, 138, 144, 144, 144, 144, 144, 144, 144, 1, 12, 57 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS This is another "Fibonacci array". LINKS Robert Israel, Table of n, a(n) for n = 0..10010 (antidiagonals 0 to 140, flattened) Richard L. Ollerton and Anthony G. Shannon, Some properties of generalized Pascal squares and triangles, Fib. Q., 36 (1998), 98-109. See Table 6. FORMULA G.f. as array: 1/((1-x-x*y)*(1-y-y^2)). - Robert Israel, Nov 22 2017 EXAMPLE The array begins: 1, 1, 2, 3, 5, 8, 13, 21, 34,... 1, 2, 3, 5, 8, 13, 21, 34, 55,... 1, 3, 5, 8, 13, 21, 34, 55, 89,... 1, 4, 8, 13, 21, 34, 55, 89, 144,... 1, 5, 12, 21, 34, 55, 89, 144, 233,... 1, 6, 17, 33, 55, 89, 144, 233, 377,... 1, 7, 23, 50, 88, 144, 233, 377, 610,... 1, 8, 30, 73, 138, 232, 377, 610, 987,... 1, 9, 38, 103, 211, 370, 609, 987, 1597,... ... The first few antidiagonals are: 1, 1,1, 1,2,2, 1,3,3,3, 1,4,5,5,5, 1,5,8,8,8,8, 1,6,12,13,13,13,13, 1,7,17,21,21,21,21,21, ... MAPLE A294453:= proc(n, k) option remember; if n = 0 then combinat:-fibonacci(k+1) elif k = 0 then 1 else procname(n-1, k-1)+procname(n-1, k) fi end proc: seq(seq(A294453(m-k, k), k=0..m), m=0..10); # Robert Israel, Nov 22 2017 MATHEMATICA T[0, k_] := Fibonacci[k + 1]; T[_, 0] = 1; T[n_, k_] := T[n, k] = T[n - 1, k - 1] + T[n - 1, k]; Table[T[n - k, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Oct 16 2020 *) CROSSREFS Cf. A000045, A001629 (sums of antidiagonals). Sequence in context: A210798 A117501 A117915 * A097094 A210870 A104726 Adjacent sequences: A294450 A294451 A294452 * A294454 A294455 A294456 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Nov 22 2017 EXTENSIONS Better definition and more terms from Robert Israel, Nov 22 2017 STATUS approved

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Last modified March 30 14:20 EDT 2023. Contains 361622 sequences. (Running on oeis4.)