A176126 Numerator of -A127276(n)/A001788(n).

-1, -1, 1, 2, 4, 13, 19, 13, 17, 43, 53, 32, 38, 89, 103, 59, 67, 151, 169, 94, 104, 229, 251, 137, 149, 323, 349, 188, 202, 433, 463, 247, 263, 559, 593, 314, 332, 701, 739, 389, 409, 859, 901, 472, 494, 1033, 1079, 563, 587, 1223, 1273, 662, 688, 1429, 1483, 769, 797, 1651, 1709, 884, 914, 1889, 1951, 1007, 1039, 2143, 2209, 1138, 1172, 2413, 2483, 1277, 1313, 2699, 2773, 1424, 1462, 3001, 3079, 1579

Offset: 0

Author

Paul Curtz, Dec 07 2010

Keywords

• sign
• frac

Comments

The sequence of fractions starts -1/0, -1/1, 1/3, 2/3, 4/5, 13/15, 19/21, 13/14, 17/18, 43/45, 53/55, 32/33, 38/39, ...

The denominators are apparently A064038(n+1) = A061041(4+8*n) (i.e., specified as numerators in A061041).

The difference between denominator and numerator is A014695(n), n > 0.

Crossrefs

Cf. A001788, A127276.

Cf. A061041, A064038, A014695.

Programs

Maple

A001788 := proc(n) n*(n+1)*2^(n-2) ; end proc:
A127276 := proc(n) 2^n-A001788(n) ; end proc:
A176126 := proc(n) if n = 0 then -1 else 2^n/A001788(n)-1 ; numer(-%) ; end if; end proc:
seq(A176126(n),n=0..40) ;

Formula

Conjecture: a(n) = +3*a(n-1) -6*a(n-2) +10*a(n-3) -12*a(n-4) +12*a(n-5) -10*a(n-6) +6*a(n-7) -3*a(n-8) +a(n-9) with g.f. (x^4-x^3+3*x^2-x+1)*(x^4-x^3-2*x^2-x+1) / ( (x-1)^3*(x^2+1)^3 ). - R. J. Mathar, Dec 12 2010

a(n) = 3*a(n-4) -3*a(n-8) +a(n-12).