Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Dec 16 2023 13:10:54
%S 1,0,1,-1,1,1,-3,0,2,1,-2,-1,1,3,1,-7,-1,1,2,4,1,-5,-4,0,3,3,5,1,-8,
%T -3,-1,1,5,4,6,1,-3,-5,-1,2,2,7,5,7,1,-13,-2,-2,1,5,3,9,6,8,1,-10,-9,
%U -1,1,3,8,4,11,7,9,1,-17,-7,-5,0,4,5,11,5,13,8,10,1,-7,-12,-4,-1,1,7,7,14,6,15,9,11,1,-18,-5,-7,-1,3,2,10,9,17,7
%N Table T(n,k), n>=0 and k>=0: Stern's diatomic array read by antidiagonals (version 5).
%F Each row is obtained by copying the previous row but interpolating the sum of pairs of adjacent terms.
%F T(n, 2*k) = T(n-1, k) = T(n, k) - A002487(k).
%F T(n, 2*k+1) = T(n, 2*k) + T(n, 2*k+2); T(0, 0)=1, T(0, 1)=0.
%F The k-th column is an arithmetic progression with : T(n, k) = T(0, k) + n* A002487(k).
%e row n=0 : 1, 0, -1, -3, -2, -7, -5, -8, -3, -13, -10, -17, -7, -18, -11, ...
%e row n=1 : 1, 1, 0, -1, -1, -4, -3, -5, -2, -9, -7, -12, -5, -13, ...
%e row n=2 : 1, 2, 1, 1, 0, -1, -1, -2, -1, -5, -4, -7, -3, ...
%e row n=3 : 1, 3, 2, 3, 1, 2, 1, 1, 0, -1, -1, -2, -1, ...
%e row n=4 : 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, ...
%Y Cf. A049456, A070878, A070879, A049455, A002487.
%K sign,tabl
%O 0,7
%A _Philippe Deléham_, Dec 30 2003