A059503 - OEIS

%I #21 Sep 15 2017 08:13:22

%S 1,2,3,3,5,9,4,7,14,27,5,9,19,40,80,6,11,24,53,114,234,7,13,29,66,148,

%T 323,677,8,15,34,79,182,412,910,1941,9,17,39,92,216,501,1143,2551,

%U 5523,10,19,44,105,250,590,1376,3161,7120,15615,11,21,49,118

%N The array in A059502 read by antidiagonals in 'up' direction.

%H G. C. Greubel, <a href="/A059503/b059503.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%F T(n,k) = ((3 - k)*Fibonacci(2*k) + (5*n + 3*k)*Fibonacci(2*k - 1))/5. - _G. C. Greubel_, Sep 10 2017

%e The array begins

%e 1 3 9 27 80 ...

%e 2 5 14 40 ...

%e 3 7 19 ...

%e 4 9 5 ...

%t T[n_, k_] := ((3 - k)*Fibonacci[2*k] + (5*n + 3*k)*Fibonacci[2*k - 1])/5;

%t TableForm[Table[T[n, k], {n, 0, 5}, {k, 1, 5}]]

%t Table[T[n - k, k + 1], {n, 0, 10}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Sep 10 2017 *)

%Y Rows give A059502, A059505, A059506, A059507, A059508; main diagonal = A059509.

%Y Cf. A000667, A059216, A059219.

%K nonn,tabl,nice,easy

%O 0,2

%A _Floor van Lamoen_, Jan 19 2001