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Array of A002450 in the top row and higher-order differences in subsequent rows, read by antidiagonals.
1

%I #8 Feb 24 2019 21:09:29

%S 0,1,1,3,4,5,9,12,16,21,27,36,48,64,85,81,108,144,192,256,341,243,324,

%T 432,576,768,1024,1365,729,972,1296,1728,2304,3072,4096,5461,2187,

%U 2916,3888,5184,6912,9216,12288,16384,21845,6561

%N Array of A002450 in the top row and higher-order differences in subsequent rows, read by antidiagonals.

%F T(0,k) = A002450(k). T(n,k) = T(n-1,k+1) - T(n-1,k), n > 0.

%e The array starts:

%e 0, 1, 5, 21, 85, 341,1365,5461,21845,87381,349525, A002450

%e 1, 4, 16, 64, 256,1024,4096,16384,65536,262144,1048576, A000302

%e 3, 12, 48, 192, 768,3072,12288,49152,196608,786432, A002001, A164346, A110594

%e 9, 36, 144, 576,2304,9216,36864,147456 A002063, A055841

%p A002450 := proc(n) (4^n-1)/3 ; end proc:

%p A166976 := proc(n,k) option remember; if n = 0 then A002450(k) else procname(n-1,k+1)-procname(n-1,k) ; end if; end proc: # _R. J. Mathar_, Jul 02 2011

%K nonn,easy,tabl

%O 0,4

%A _Paul Curtz_, Oct 26 2009