A134662 Number of odd coefficients in (1 + x + x^4)^n.

1, 3, 3, 9, 3, 7, 9, 17, 3, 9, 7, 21, 9, 17, 17, 33, 3, 9, 9, 27, 7, 17, 21, 43, 9, 27, 17, 51, 17, 35, 33, 67, 3, 9, 9, 27, 9, 21, 27, 51, 7, 21, 17, 51, 21, 41, 43, 83, 9, 27, 27, 81, 17, 43, 51, 113, 17, 51, 35, 105, 33, 67, 67, 137, 3, 9, 9, 27, 9, 21, 27, 51, 9, 27, 21, 63, 27, 51

Offset

0,2

Links

Table of n, a(n) for n=0..77.

S. R. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654)

Example

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;
3,9;
3,7,9,17;
3,9,7,21,9,17,17,33;
3,9,9,27,7,17,21,43,9,27,17,51,17,35,33,67;
3,9,9,27,9,21,27,51,7,21,17,51,21,41,43,83,9,27,27,81,17,43,51,113,17,51,35,105,33,67,67,137;
Thanks to Michel Marcus we can see the first few terms of the next four rows as shown below:
3,9,9,27,9,21,27,51,9,27,21,63,27,51,51,99,7,21,...
3,9,9,27,9,21,27,51,9,27,21,63,27,51,51,99,9,27,27,...
3,9,9,27,9,21,27,51,9,27,21,63,27,51,51,99,9,27,27,81,...
3,9,9,27,9,21,27,51,9,27,21,63,27,51,51,99,9,27,27,81,21,...
...
Apparently in each row the first quarter of the terms (and no more) are equal to 3 times the beginning of the sequence itself (comment corrected after Sloane's comment in A247649, Mar 03 2015).
(End)

Mathematica

Table[PolynomialMod[(1+x+x^4)^n, 2]/.x->1, {n, 0, 80}]
Table[Count[CoefficientList[Expand[(1+x+x^4)^n], x], _?OddQ], {n, 0, 80}] (* Harvey P. Dale, Apr 15 2012 *)

Prog

(PARI) a(n) = {my(pol = (xx^4 + xx + 1)*Mod(1, 2)); subst(lift(pol^n), xx, 1); } \\ Michel Marcus, Mar 01 2015
(PARI) tabf(nn, k=16) = {nbpt = 0; for (n=0, nn, if (n==0, nbt = 1, nbt = 2^(n-1)); for (m=nbpt, nbpt+nbt-1, if (m-nbpt >k, k++; break); print1(nbopd(m), ", "); ); print(); nbpt += nbt; ); } \\ Michel Marcus, Mar 03 2015

Crossrefs

Cf. A071053.

Sequence in context: A074724 A109932 A071909 * A145444 A165824 A256689

Adjacent sequences: A134659 A134660 A134661 * A134663 A134664 A134665

Keyword

nonn

Author

Steven Finch, Jan 25 2008

Extensions

First Mathematica program corrected by Harvey P. Dale, Apr 15 2012

Status

approved