A116578 - OEIS

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

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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}