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A116578 Integerization of a truncated Pascal root structure with a power of two level pumping. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A300328 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

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Last modified February 27 19:23 EST 2020. Contains 332308 sequences. (Running on oeis4.)