|
| |
|
|
A141666
|
|
A symmetrical triangle of coefficients based on A004018 (or number of ways of writing n as a sum of 2 squares): t(n,m)=r2(n-m+1)*r2(m+1).
|
|
0
| |
|
|
1, 4, 4, 4, 16, 4, 0, 16, 16, 0, 4, 0, 16, 0, 4, 8, 16, 0, 0, 16, 8, 0, 32, 16, 0, 16, 32, 0, 0, 0, 32, 0, 0, 32, 0, 0, 4, 0, 0, 0, 16, 0, 0, 0, 4, 4, 16, 0, 0, 32, 32, 0, 0, 16, 4, 8, 16, 16, 0, 0, 64, 0, 0, 16, 16, 8
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Row sums are:
{1, 8, 24, 32, 24, 48, 96, 64, 24, 104, 144}.
|
|
|
REFERENCES
| http : // mathworld.wolfram.com/SumofSquaresFunction.html
G. E. Andrews, Number Theory, 1971, Dover Publications New York, p 44,p 201-207.
|
|
|
FORMULA
| t(n,m)=r2(n-m+1)*r2(m+1).
|
|
|
EXAMPLE
| {1},
{4, 4},
{4, 16, 4},
{0, 16, 16, 0},
{4, 0, 16, 0, 4},
{8, 16, 0, 0, 16, 8},
{0, 32, 16, 0, 16, 32, 0},
{0, 0, 32, 0, 0, 32, 0, 0},
{4, 0, 0, 0, 16, 0, 0, 0, 4},
{4, 16, 0, 0, 32, 32, 0, 0, 16, 4},
{8, 16, 16, 0, 0, 64, 0, 0, 16, 16, 8}
|
|
|
MATHEMATICA
| Clear[a] a = Table[SeriesCoefficient[Series[1 + 4Sum[(-1)^(1 + n)/(-1 + x^(1 - 2*n)), {n, 100}], {x, 0, 100}], n], {n, 0, 100}]; Table[Table[a[[n - m + 1]]*a[[m + 1]], {m, 0, n}], {n, 0, 10}]; Flatten[%]
|
|
|
CROSSREFS
| Cf. A004018.
Sequence in context: A170897 A179526 A098525 * A102127 A201625 A131946
Adjacent sequences: A141663 A141664 A141665 * A141667 A141668 A141669
|
|
|
KEYWORD
| nonn,uned
|
|
|
AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 05 2008
|
| |
|
|
