A084178 Inverse binomial transform of Fibonacci oblongs.

0, 1, 0, 3, -1, 10, -7, 35, -36, 127, -165, 474, -715, 1807, -3004, 6995, -12393, 27370, -50559, 107883, -204820, 427351, -826045, 1698458, -3321891, 6765175, -13333932, 26985675, -53457121, 107746282, -214146295, 430470899, -857417220, 1720537327, -3431847189

Offset: 0

Author

Paul Barry, May 18 2003

Keywords

• easy
• sign

Comments

Inverse binomial transform of A001654.

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,3,2).

Crossrefs

Cf. A000045, A052964, A084179.

Programs

Mathematica

LinearRecurrence[{-1,3,2},{0,1,0},40] (* Harvey P. Dale, Nov 24 2020 *)

Formula

a(n)=((1/2+sqrt(5)/2)^(n+1)+(1/2-sqrt(5)/2)^(n+1)-(-2)^n)/5;

G.f.: x(1+x)/(1+x-3x^2-2x^3)=x(1-x)/((1+2x)(1-x-x^2)).

a(n) = A084179(n)+A084179(n-1). - R. J. Mathar, Dec 10 2014