A134659 Total number of odd coefficients in (1+x+x^2)^k for k=0,...,n.

1, 4, 7, 12, 15, 24, 29, 40, 43, 52, 61, 76, 81, 96, 107, 128, 131, 140, 149, 164, 173, 200, 215, 248, 253, 268, 283, 308, 319, 352, 373, 416, 419, 428, 437, 452, 461, 488, 503, 536, 545, 572, 599, 644, 659, 704, 737, 800, 805, 820, 835, 860, 875, 920, 945, 1000

Offset: 0

Author

Steven Finch, Jan 25 2008

Keywords

• nonn

Comments

a(n) = Sum_{k <= n} A071053(k)

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..16383
• S. R. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654)
• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015

Crossrefs

Cf. A001316, A006046, A027907, A071053.

Programs

Mathematica

Sum[PolynomialMod[(1+x+x^2)^k, 2] /. x->1, {k, 0, n-1}]

Extensions

Offset changed to 0 by N. J. A. Sloane, Feb 06 2015