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A155124 Triangle T(n, k) = 1-n if k=0 else 2, read by rows. 2
1, 0, 2, -1, 2, 2, -2, 2, 2, 2, -3, 2, 2, 2, 2, -4, 2, 2, 2, 2, 2, -5, 2, 2, 2, 2, 2, 2, -6, 2, 2, 2, 2, 2, 2, 2, -7, 2, 2, 2, 2, 2, 2, 2, 2, -8, 2, 2, 2, 2, 2, 2, 2, 2, 2, -9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -11, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

These polynomials in n are column functions for general Pascal-Sierpinski triangles.

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

Let p(x,m) = (1-m) + 2*x*(1-x^m)/(1-x) then the triangle is given by T(n, k) = coefficients( p(x,n) ).

Coefficient triangle of polynomial: p(x,n)= 1-m + 2*Sum_{k=1..n} x^k.

From G. C. Greubel, Mar 25 2021: (Start)

T(n, k) = 1-n if k=0 else 2.

Sum_{k=0..n} T(n ,k) = n+1 = A000027(n+1). (End)

EXAMPLE

Triangle begins as:

   1;

   0, 2;

  -1, 2, 2;

  -2, 2, 2, 2;

  -3, 2, 2, 2, 2;

  -4, 2, 2, 2, 2, 2;

  -5, 2, 2, 2, 2, 2, 2;

  -6, 2, 2, 2, 2, 2, 2, 2;

  -7, 2, 2, 2, 2, 2, 2, 2, 2;

  -8, 2, 2, 2, 2, 2, 2, 2, 2, 2;

  -9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2;

MATHEMATICA

Table[CoefficientList[-(m-1) + 2*x*(1-x^m)/(1-x), x], {m, 0, 15}]//Flatten

Table[If[k==0, 1-n, 2], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 25 2021 *)

PROG

(Magma) [k eq 0 select 1-n else 2: k in [0..n], n in [0..15]]; // G. C. Greubel, Mar 25 2021

(Sage) flatten([[1-n if k==0 else 2 for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Mar 25 2021

CROSSREFS

Sequence in context: A339932 A254690 A156642 * A138033 A283876 A067754

Adjacent sequences:  A155121 A155122 A155123 * A155125 A155126 A155127

KEYWORD

sign

AUTHOR

Roger L. Bagula, Jan 20 2009

EXTENSIONS

Edited by G. C. Greubel, Mar 25 2021

STATUS

approved

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Last modified April 11 21:23 EDT 2021. Contains 342888 sequences. (Running on oeis4.)