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Rectangular array read by upward antidiagonals: A(n,k) = n-2+k*2^(n-3), n>=3, k>=0.
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%I #7 Jan 20 2014 15:50:45

%S 1,2,2,3,4,3,4,7,6,4,5,12,11,8,5,6,21,20,15,10,6,7,38,37,28,19,12,7,8,

%T 71,70,53,36,23,14,8,9,136,135,102,69,44,27,16,9,10,265,264,199,134,

%U 85,52,31,18,10,11,522,521,392,263,166,101,60,35,20,11

%N Rectangular array read by upward antidiagonals: A(n,k) = n-2+k*2^(n-3), n>=3, k>=0.

%C Row index n begins with 3, column index k begins with 0.

%C Conjectured equivalence classes associated with the row entries of A233332.

%F Conjecture: G.f. for row n is F_n(x) = ((n-2)+(2^(n-3)-(n-2))*x)/(1-x)^2 = ((n-2)+(2^(n-3)-(n-3)-1)*x)/(1-x)^2 = ((n-2)+A000295(n-3)*x)/(1-x)^2, n>=3.

%F Conjecture: G.f. for column k is G_k(x) = (k+1-2*(k+1)*x+k*x^2)/((1-2*x)*(1-x)^2), k>=0.

%e Array begins:

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

%e 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...

%e 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, ...

%e 4, 12, 20, 28, 36, 44, 52, 60, 68, 76, ...

%e 5, 21, 37, 53, 69, 85, 101, 117, 133, 149, ...

%e 6, 38, 70, 102, 134, 166, 198, 230, 262, 294, ...

%e 7, 71, 135, 199, 263, 327, 391, 455, 519, 583, ...

%e 8, 136, 264, 392, 520, 648, 776, 904, 1032, 1160, ...

%e 9, 265, 521, 777, 1033, 1289, 1545, 1801, 2057, 2313, ...

%e 10, 522, 1034, 1546, 2058, 2570, 3082, 3594, 4106, 4618, ...

%Y Cf. A000295, A132925 (conjectured antidiagonal sums), A233332.

%K nonn,tabl

%O 3,2

%A _L. Edson Jeffery_, Jan 16 2014