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Rectangular array A read by upward antidiagonals in which row n is the set of positive integers that are congruent to {(1 + 2^n*(3 + 2*(-1)^n))/3, 2^(n + 1), (1 + 2^n*(15 + 2*(-1)^n))/3} (mod 2^(n+2)).
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%I #12 Nov 05 2015 14:32:17

%S 1,7,4,3,8,5,27,16,15,9,11,32,19,23,12,107,64,59,35,24,13,43,128,75,

%T 91,48,31,17,427,256,235,139,96,51,39,20,171,512,299,363,192,123,67,

%U 40,21,1707,1024,939,555,384,203,155,80,47,25

%N Rectangular array A read by upward antidiagonals in which row n is the set of positive integers that are congruent to {(1 + 2^n*(3 + 2*(-1)^n))/3, 2^(n + 1), (1 + 2^n*(15 + 2*(-1)^n))/3} (mod 2^(n+2)).

%F A(n,k) = A(n,k-3) + 2^(n+2), n >= 1, k > 3, with initial conditions A(n,1) = (1 + 2^n*(3 + 2*(-1)^n))/3, A(n,2) = 2^(n+1), A(n,3) = A(n,1) + 2^(n+1).

%F A(n,k) == (1 + 2^n*(3 + 2*(-1)^n))/3 (mod 2^(n+1) or 2^(n+1) (mod 2^(n+2)).

%e Array A begins:

%e . 1 4 5 9 12 13 17 20 21 25

%e . 7 8 15 23 24 31 39 40 47 55

%e . 3 16 19 35 48 51 67 80 83 99

%e . 27 32 59 91 96 123 155 160 187 219

%e . 11 64 75 139 192 203 267 320 331 395

%e . 107 128 235 363 384 491 619 640 747 875

%e . 43 256 299 555 768 811 1067 1280 1323 1579

%e . 427 512 939 1451 1536 1963 2475 2560 2987 3499

%e . 171 1024 1195 2219 3072 3243 4267 5120 5291 6315

%e . 1707 2048 3755 5803 6144 7851 9899 10240 11947 13995

%t (* Array antidiagonals flattened: *)

%t a[n_, 1] := (1 + 2^n*(3 + 2*(-1)^n))/3; a[n_, 2] := 2^(n + 1); a[n_, 3] := a[n, 1] + 2^(n + 1); a[n_, k_] := a[n, k - 3] + 2^(n + 2); Flatten[Table[a[n - k + 1, k], {n, 10}, {k, n}]]

%Y A047610 (row 1).

%K nonn,tabl

%O 1,2

%A _L. Edson Jeffery_, May 04 2015