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A155123 Six levels of the coefficient triangle of the Pascal-Sierpinski functions. 0
1, 2, 2, 2, 0, 4, 4, 0, -4, 8, 12, 0, 8, -32, 8, 48 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are 2^(n+1);

{1, 2, 4, 8, 16, 32,...}.

LINKS

Table of n, a(n) for n=0..15.

FORMULA

Triangle:

{{1},

{1, 1},

{1, 2*n, 1},

{1, f[n], f[n], 1},

{1, g[n], 6 + 24 *(n - 1) + 28*(n - 1)^2 + 8* ( n - 1)^3, g[n], 1},

{1, h[n], k[n - 1] - h[n] - 1, k[n - 1] - h[n] - 1, h[n], 1}}

f[n_]=3*n^2 - (n - 1)^2;

g[n_]=-2 + 2 *n + 2* n^2 + 2 n^3;

h[n_]=-3 + 2 n + 2 n^2 + 2 n^3 + 2*n^4;

k[n_]=16+ 80 n + 140 *n^2 + 100*n^3 + 24* n^4;

These functions and the triangles they make are general Pascal-Sierpinski

functions.

EXAMPLE

{1},

{2},

{2, 2},

{0, 4, 4},

{0, -4, 8, 12},

{0, 8, -32, 8, 48}

MATHEMATICA

a1 = {{1},

{1, 1},

{1, 2 *n, 1},

{1, -1 + 2 *n + 2 n^2, -1 + 2 n + 2 n^2, 1},

{1, -2 + 2 *n + 2 n^2 + 2 n^3, 2 - 8 n + 4 n^2 + 8 n^3, -2 + 2* n + 2 n^2 + 2 n^3, 1},

{1, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, 2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 1}}

Table[CoefficientList[Apply[Plus, a1[[m]]], n], {m, 1, Length[a1]}];

Flatten[%]

CROSSREFS

A142463

Sequence in context: A263527 A261444 A000091 * A125938 A215461 A158851

Adjacent sequences:  A155120 A155121 A155122 * A155124 A155125 A155126

KEYWORD

tabl,uned,sign

AUTHOR

Roger L. Bagula, Jan 20 2009

STATUS

approved

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Last modified March 29 21:48 EDT 2017. Contains 284288 sequences.