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Search: id:A158106
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| A158106 |
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A triangle of structure called "Polynomial on residue classes" (PORC) in 1960 by Higman from Britt Witty's Ph.D. thesis. |
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1
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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REFERENCES
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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)
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EXAMPLE
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{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}}
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MATHEMATICA
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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]
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CROSSREFS
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A158079
Sequence in context: A008280 A063960 A025510 this_sequence A069896 A053246 A157123
Adjacent sequences: A158103 A158104 A158105 this_sequence A158107 A158108 A158109
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 12 2009
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