%I #19 Feb 10 2016 23:14:33

%S 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 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 23,3,1,1,1,10,1,57,37,131,1,94,21,5,1,1,1,11

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

%C 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 Chai Wah Wu, <a href="/A260534/b260534.txt">Table of n, a(n) for n = 0..10010</a>

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SternsDiatomic">Rational Trees and Binary Partitions</a>.

%e Array starts:

%e n\k[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

%e [0] 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e [1] 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, ... [A002487]

%e [2] 1, 1, 3, 1, 7, 5, 11, 1, 23, 21, 59, ... [A101624]

%e [3] 1, 1, 4, 1, 13, 10, 31, 1, 94, 91, 355, ...

%e [4] 1, 1, 5, 1, 21, 17, 69, 1, 277, 273, 1349, ... [A101625]

%e [5] 1, 1, 6, 1, 31, 26, 131, 1, 656, 651, 3881, ...

%e [6] 1, 1, 7, 1, 43, 37, 223, 1, 1339, 1333, 9295, ...

%e [7] 1, 1, 8, 1, 57, 50, 351, 1, 2458, 2451, 19559, ...

%e [8] 1, 1, 9, 1, 73, 65, 521, 1, 4169, 4161, 37385, ...

%e -,-,-,-,A002061,A002522,A071568,-,-,A059826,-,A002523,

%p T := (n,k) -> add(modp(binomial(k-j,j),2)*n^j, j=0..k):

%p seq(lprint(seq(T(n,k),k=0..10)),n=0..5);

%t 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 (Python)

%o def A260534_T(n,k):

%o return sum(0 if ~(k-j) & j else n**j for j in range(k+1)) # _Chai Wah Wu_, Feb 08 2016

%Y Cf. A002061, A002487, A002522, A002523, A059826, A071568, A101624, A101625.

%K nonn,tabl

%O 0,9

%A _Peter Luschny_, Sep 20 2015