A158106 A triangle of structure called "Polynomial on residue classes" (PORC) in 1960 by Higman from Britt Witty's Ph.D. thesis.

1, 2, 2, 5, 5, 5, 14, 14, 15, 15, 51, 51, 67, 76, 77, 267, 267, 504, 633, 684, 731, 2328, 2328, 9310, 9310, 34297, 62440, 113147

Offset

1,2

Comments

Row sums are:

{1, 4, 15, 58, 322, 3086, 233160,...}.

This is my best effort to translate code the pages 3 and 4 of the thesis

downloaded from:

http://www.brettwitty.net/maths/phd/

http://www.brettwitty.net/maths/phd/bw-thesis.pdf

References

Marcus Du Sautoy, Symmetry: A Journey into the Patterns of Nature,Harper (March 11, 2008),page 96,pp. 141-143 ( and the work of Christopher Voll)

Links

Table of n, a(n) for n=1..28.

Example

{1},
{2, 2},
{5, 5, 5},
{14, 14, 15, 15},
{51, 51, 67, 76, 77},
{267, 267, 504, 633, 684, 731},
{2328, 2328, 9310, 9310, 34297, 62440, 113147}}

Mathematica

Clear[p, x, n, a];
p[x_, 1] := 1; p[x_, 2] := 2; p[x_, 3] := 5;
p[x_, 4] := If[x <= 2, 14, 15];
p[x_, 5] := If[x <= 2, 51, If[x == 3, 67, 61 + 2*x + 2 * GCD[x - 1, 3] + GCD[x - 1, 4]]];
p[x_, 6] := If[x <= 2, 267, If[x == 3, 504, 3*x^2 + 39*x + 344 + 24 *GCD[x - 1, 3] + 11* GCD[x - 1, 4] + 2* GCD[x - 1, 5]]];
p[x_, 7] := If[x <= 2, 2328, If[x >= 3 and x<5, 9310, If[x == 5, 34297,
3*x^5 + 12*x^4 + 44*x^3 + 170*x^2 + 707* x + 2455 + (4*x^2 + 44*x + 291) *GCD[x - 1, 3] + (x^2 + 19*x + 135) * GCD[x - 1, 4] + (3*x + 31)* GCD[x - 1, 5] + 4* GCD[ x - 1, 7] + 5* GCD[x - 1, 8] + GCD[x - 1, 9]]]];
a = Table[Table[p[x, n], {x, 1, n}], {n, 1, 7}];
Flatten[a]

Crossrefs

A158079

Sequence in context: A350172 A356387 A172417 * A185313 A208301 A069896

Adjacent sequences: A158103 A158104 A158105 * A158107 A158108 A158109

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 12 2009

Status

approved