A294677 G.f.: 1 + Sum_{n=-oo..+oo, n<>0} (x - x^n)^n / (1 - (x - x^n)^n).

1, -1, 2, -3, 7, -11, 17, -21, 35, -67, 125, -179, 246, -384, 715, -1199, 1871, -2850, 4593, -7589, 12811, -20366, 31545, -50483, 84597, -138964, 222534, -352910, 569680, -931694, 1523165, -2451150, 3924137, -6331780, 10329289, -16804843, 27109912, -43594466, 70485938, -114450985, 185713588, -300089184, 484106880, -782672321, 1269075821, -2056723036, 3325362211, -5371243069, 8688055226

Offset

0,3

Comments

Compare g.f. to: Sum_{n=-oo..+oo} (x - x^(n+1))^n = 0.

Compare g.f. to: Sum_{n=-oo..+oo, n<>0} x^n/(1 - x^n) = 0, ignoring constant terms.

Limit a(n+1)/a(n) = -(sqrt(5) + 1)/2.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Formula

a(n) ~ (-1)^n * (1 + sqrt(5))^(n+1) / 2^(n+2). - Vaclav Kotesovec, Nov 08 2017

Example

G.f.: A(x) = 1 - x + 2*x^2 - 3*x^3 + 7*x^4 - 11*x^5 + 17*x^6 - 21*x^7 + 35*x^8 - 67*x^9 + 125*x^10 - 179*x^11 + 246*x^12 - 384*x^13 + 715*x^14 - 1199*x^15 + 1871*x^16 - 2850*x^17 + 4593*x^18 - 7589*x^19 + 12811*x^20 - 20366*x^21 + 31545*x^22 - 50483*x^23 + 84597*x^24 - 138964*x^25 +...

Prog

(PARI) {a(n) = my(A); A = sum(m=-n-1, n+1, if(m==0, 1, (x-x^m)^m/(1 - (x-x^m +x*O(x^n))^m ))); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A290003.

Sequence in context: A375818 A155141 A127944 * A274161 A045324 A140460

Adjacent sequences: A294674 A294675 A294676 * A294678 A294679 A294680

Keyword

sign

Author

Paul D. Hanna, Nov 07 2017

Status

approved