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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).
1
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, 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, 23, 3, 1, 1, 1, 10, 1, 57, 37, 131, 1, 94, 21, 5, 1, 1, 1, 11
OFFSET
0,9
COMMENTS
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.)
EXAMPLE
Array starts:
n\k[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
[0] 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
[1] 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, ... [A002487]
[2] 1, 1, 3, 1, 7, 5, 11, 1, 23, 21, 59, ... [A101624]
[3] 1, 1, 4, 1, 13, 10, 31, 1, 94, 91, 355, ...
[4] 1, 1, 5, 1, 21, 17, 69, 1, 277, 273, 1349, ... [A101625]
[5] 1, 1, 6, 1, 31, 26, 131, 1, 656, 651, 3881, ...
[6] 1, 1, 7, 1, 43, 37, 223, 1, 1339, 1333, 9295, ...
[7] 1, 1, 8, 1, 57, 50, 351, 1, 2458, 2451, 19559, ...
[8] 1, 1, 9, 1, 73, 65, 521, 1, 4169, 4161, 37385, ...
MAPLE
T := (n, k) -> add(modp(binomial(k-j, j), 2)*n^j, j=0..k):
seq(lprint(seq(T(n, k), k=0..10)), n=0..5);
MATHEMATICA
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 *)
PROG
(Python)
def A260534_T(n, k):
return sum(0 if ~(k-j) & j else n**j for j in range(k+1)) # Chai Wah Wu, Feb 08 2016
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 20 2015
STATUS
approved