A116578 Integerization of a truncated Pascal root structure with a power of two level pumping.

2, 0, 4, 4, 4, 8, 0, 11, 11, 16, 9, 9, 25, 25, 32, 0, 31, 31, 55, 55, 64, 28, 28, 79, 79, 115, 115, 128, 0, 97, 97, 181, 181, 236, 236, 255, 88, 88, 256, 256, 392, 392, 481, 481, 512, 0, 316, 316, 601, 601, 828, 828, 973, 973, 1024

Offset

0,1

Comments

I used a backward representation of the roots so that the least comes first: the results behaves like an economics or population curve. When taken as Modulo two one can see a pattern like that of Pascal's triangle in the zeros and ones. The alternating (t-1)^n polynomials are solved as: (t-1)^n=1 and instead of the 2^n coefficients, the roots are used for sequence. It is a unique new approach to the problem of Pascal's triangle.

Links

Table of n, a(n) for n=0..54.

Formula

a(n) = Table[Table[Floor[2^(n - 1)*Abs[x]] /. NSolve[(x - 1)^n - 1 == 0.x][[m]], {m, n, 1, -1}], {n, 1, 10}]

Example

Triangular form of the sequence:
{2}
{0, 4}
{4, 4, 8}
{0, 11, 11, 16}
{9, 9, 25, 25, 32}
{0, 31, 31, 55, 55, 64}

Mathematica

Table[Table[Floor[2^(n - 1)*Abs[x]] /. NSolve[(x - 1)^n - 1 == 0.x][[m]], {m, n, 1, -1}], {n, 1, 10}] Flatten[a]

Crossrefs

Sequence in context: A365382 A200291 A049797 * A078050 A134271 A094403

Adjacent sequences: A116575 A116576 A116577 * A116579 A116580 A116581

Keyword

nonn,uned,obsc

Author

Roger L. Bagula, Mar 21 2006

Status

approved