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, 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.)

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10010

Peter Luschny, Rational Trees and Binary Partitions.

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, ...
-,-,-,-,A002061,A002522,A071568,-,-,A059826,-,A002523,

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

Crossrefs

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

Sequence in context: A107682 A349703 A178239 * A350103 A085476 A124944

Adjacent sequences: A260531 A260532 A260533 * A260535 A260536 A260537

Keyword

nonn,tabl

Author

Peter Luschny, Sep 20 2015

Status

approved