A134661 Number of odd coefficients in (1 + x + x^3)^n.

1, 3, 3, 7, 3, 9, 7, 13, 3, 9, 9, 19, 7, 21, 13, 27, 3, 9, 9, 21, 9, 27, 19, 35, 7, 21, 21, 41, 13, 39, 27, 55, 3, 9, 9, 21, 9, 27, 21, 39, 9, 27, 27, 55, 19, 57, 35, 73, 7, 21, 21, 49, 21, 63, 41, 75, 13, 39, 39, 79, 27, 81, 55, 109, 3, 9, 9, 21, 9, 27, 21, 39, 9, 27, 27, 57, 21, 63, 39

Offset: 0

Author

Steven Finch, Jan 25 2008

Keywords

• nonn

Examples

			From _Omar E. Pol_, Mar 01 2015: (Start)
Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
3;
3,7;
3,9,7,13;
3,9,9,19,7,21,13,27;
3,9,9,21,9,27,19,35,7,21,21,41,13,39,27,55;
3,9,9,21,9,27,21,39,9,27,27,55,19,57,35,73,7,21,21,49,21,63,41,75,13,39,39,79,27,81,55,109;
3,9,9,21,9,27,21,39,9,27,27,57,21,63,39...
...
Note that in each row a fraction of the first terms are equal to 3 times the beginning of the sequence itself. For rows 0-6 the fractions are: 0, 1, 1/2, 1/2, 3/8, 3/8, 11/32. Apparently the fractions converge to a constant.
(End)
		

Links

• Joerg Arndt, Table of n, a(n) for n = 0..10000
• S. R. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle, arXiv:0802.2654 [math.NT], 2008.

Crossrefs

Cf. A071053, A038717.

Programs

Mathematica

PolynomialMod[(1+x+x^3)^n, 2] /. x->1

PARI

a(n) = {my(pol= Pol([1,0,1,1], xx)*Mod(1,2)); subst(lift(pol^n), xx, 1);} \\ Michel Marcus, Mar 01 2015