|
| |
|
|
A322213
|
|
a(n) = coefficient of x^n*y^n in Product_{n>=1} (1 - (x^n + y^n)).
|
|
4
|
|
|
|
1, 0, 0, -2, -2, -2, 0, 2, 2, 4, -2, 2, 0, 4, -2, 4, 6, 4, 4, -2, -10, -12, -12, -16, -14, 6, 6, -4, 16, 22, 30, 12, 18, -60, -18, -34, -64, -56, -36, -46, 16, 46, 64, 70, 110, 192, 152, 124, 58, 78, -26, -54, -366, -278, -182, -282, -190, 40, -112, 234, 300, 476, 488, 906, 732, 616, 706, 154, 228, -180, -864, -1112, -1744, -2294, -2824, -3154, -2170, -2146, -2524, -1102, -476, -126, 1986, 4338, 3344, 3608, 6316, 5136, 6638, 6726, 5254, 3982, 2916, -1466, -86, -6710, -6502, -9900, -9128, -14170, -12232, -13940, -9192, -6892, -6270, 3762, 7058, 9468, 23860, 22556, 29812, 40150, 34952, 30350
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
G.f.: A(x) = 1 - 2*x^3 - 2*x^4 - 2*x^5 + 2*x^7 + 2*x^8 + 4*x^9 - 2*x^10 + 2*x^11 + 4*x^13 - 2*x^14 + 4*x^15 + 6*x^16 + 4*x^17 + 4*x^18 - 2*x^19 - 10*x^20 + ...
RELATED SERIES.
The product P(x,y) = Product_{n>=1} (1 - (x^n + y^n)) begins
P(x,y) = 1 + (-1*x - 1*y) + (-1*x^2 + 0*x*y - 1*y^2) + (0*x^3 + 1*x^2*y + 1*x*y^2 + 0*y^3) + (0*x^4 + 1*x^3*y + 0*x^2*y^2 + 1*x*y^3 + 0*y^4) + (1*x^5 + 1*x^4*y + 1*x^3*y^2 + 1*x^2*y^3 + 1*x*y^4 + 1*y^5) + (0*x^6 + 0*x^5*y + 0*x^4*y^2 - 2*x^3*y^3 + 0*x^2*y^4 + 0*x*y^5 + 0*y^6) + (1*x^7 + 0*x^6*y + 0*x^5*y^2 + 0*x^4*y^3 + 0*x^3*y^4 + 0*x^2*y^5 + 0*x*y^6 + 1*y^7) + (0*x^8 - 1*x^7*y + 0*x^6*y^2 - 1*x^5*y^3 - 2*x^4*y^4 - 1*x^3*y^5 + 0*x^2*y^6 - 1*x*y^7 + 0*y^8) + (0*x^9 - 1*x^8*y - 1*x^7*y^2 - 2*x^6*y^3 - 1*x^5*y^4 - 1*x^4*y^5 - 2*x^3*y^6 - 1*x^2*y^7 - 1*x*y^8 + 0*y^9) + (0*x^10 - 1*x^9*y + 0*x^8*y^2 + 0*x^7*y^3 + 1*x^6*y^4 - 2*x^5*y^5 + 1*x^4*y^6 + 0*x^3*y^7 + 0*x^2*y^8 - 1*x*y^9 + 0*y^10) + (0*x^11 - 1*x^10*y - 1*x^9*y^2 + 0*x^8*y^3 - 1*x^7*y^4 + 0*x^6*y^5 + 0*x^5*y^6 - 1*x^4*y^7 + 0*x^3*y^8 - 1*x^2*y^9 - 1*x*y^10 + 0*y^11) + (-1*x^12 - 1*x^11*y + 0*x^10*y^2 + 0*x^9*y^3 - 1*x^8*y^4 + 0*x^7*y^5 + 0*x^6*y^6 + 0*x^5*y^7 - 1*x^4*y^8 + 0*x^3*y^9 + 0*x^2*y^10 - 1*x*y^11 - 1*y^12) + ...
in which this sequence equals the coefficients of x^n*y^n for n >= 0.
|
|
|
PROG
|
(PARI)
{P = prod(n=1, 121, (1 - (x^n + y^n) +O(x^121) +O(y^121)) ); }
{a(n) = polcoeff( polcoeff( P, n, x), n, y)}
for(n=0, 120, print1( a(n), ", ") )
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
