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A260534 Square array read by ascending antidiagonals, T(n,k) = Sum_{j=0..k} n^j*(C(k-j,j) mod 2).

%I A260534 #19 Feb 10 2016 23:14:33
%S A260534 1,1,1,1,1,1,1,1,2,1,1,1,3,1,1,1,1,4,1,3,1,1,1,5,1,7,2,1,1,1,6,1,13,5,
%T A260534 3,1,1,1,7,1,21,10,11,1,1,1,1,8,1,31,17,31,1,4,1,1,1,9,1,43,26,69,1,
%U A260534 23,3,1,1,1,10,1,57,37,131,1,94,21,5,1,1,1,11
%N A260534 Square array read by ascending antidiagonals, T(n,k) = Sum_{j=0..k} n^j*(C(k-j,j) mod 2).
%C A260534 A parametrization of Stern's diatomic series (which is here T(1,k)). (For other generalizations of Dijkstra's fusc function see the Luschny link.)
%H A260534 Chai Wah Wu, <a href="/A260534/b260534.txt">Table of n, a(n) for n = 0..10010</a>
%H A260534 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SternsDiatomic">Rational Trees and Binary Partitions</a>.
%e A260534 Array starts:
%e A260534 n\k[0, 1,  2, 3,  4,  5,   6, 7,    8,    9,    10]
%e A260534 [0] 1, 1,  1, 1,  1,  1,   1, 1,    1,    1,     1, ...
%e A260534 [1] 1, 1,  2, 1,  3,  2,   3, 1,    4,    3,     5, ... [A002487]
%e A260534 [2] 1, 1,  3, 1,  7,  5,  11, 1,   23,   21,    59, ... [A101624]
%e A260534 [3] 1, 1,  4, 1, 13, 10,  31, 1,   94,   91,   355, ...
%e A260534 [4] 1, 1,  5, 1, 21, 17,  69, 1,  277,  273,  1349, ... [A101625]
%e A260534 [5] 1, 1,  6, 1, 31, 26, 131, 1,  656,  651,  3881, ...
%e A260534 [6] 1, 1,  7, 1, 43, 37, 223, 1, 1339, 1333,  9295, ...
%e A260534 [7] 1, 1,  8, 1, 57, 50, 351, 1, 2458, 2451, 19559, ...
%e A260534 [8] 1, 1,  9, 1, 73, 65, 521, 1, 4169, 4161, 37385, ...
%e A260534 -,-,-,-,A002061,A002522,A071568,-,-,A059826,-,A002523,
%p A260534 T := (n,k) -> add(modp(binomial(k-j,j),2)*n^j, j=0..k):
%p A260534 seq(lprint(seq(T(n,k),k=0..10)),n=0..5);
%t A260534 Table[If[(n - k) == 0, 1, Sum[(n - k)^j Mod[Binomial[k - j, j], 2], {j, 0, k}]], {n, 0, 10}, {k, 0, n}] (* _Michael De Vlieger_, Sep 21 2015 *)
%o A260534 (Python)
%o A260534 def A260534_T(n,k):
%o A260534     return sum(0 if ~(k-j) & j else n**j for j in range(k+1)) # _Chai Wah Wu_, Feb 08 2016
%Y A260534 Cf. A002061, A002487, A002522, A002523, A059826, A071568, A101624, A101625.
%K A260534 nonn,tabl
%O A260534 0,9
%A A260534 _Peter Luschny_, Sep 20 2015