A138268 Negative of the Hankel transform of C(n) - C(n+2), where C = A000108.

1, 4, -17, 17, 72, -305, 305, 1292, -5473, 5473, 23184, -98209, 98209, 416020, -1762289, 1762289, 7465176, -31622993, 31622993, 133957148, -567451585, 567451585, 2403763488, -10182505537, 10182505537, 43133785636, -182717648081, 182717648081, 774004377960

Offset: 0

Author

Paul Barry, Mar 10 2008

Keywords

• easy
• sign
• changed

Comments

-a(n) is the Hankel transform of C(n)-C(n+2).

Links

• Index entries for linear recurrences with constant coefficients, signature (-3,-8,-3,-1).

Crossrefs

Cf. A000045, A000108, A001076.

Programs

Mathematica

LinearRecurrence[{-3,-8,-3,-1},{1,4,-17,17},41] (* or *) CoefficientList[ Series[(1+7x+3x^2+x^3)/(1+3x+8x^2+3x^3+x^4),{x,0,40}],x] (* Harvey P. Dale, May 26 2011 *)

Formula

G.f.: (1+7*x+3*x^2+x^3)/(1+3*x+8*x^2+3*x^3+x^4).

a(n) = (Fibonacci(3*floor((2*n+5)/3))/Fibonacci(3))*(4*sin(2*Pi*n/3+Pi/6)/3+1/3).

a(0)=1, a(1)=4, a(2)=-17, a(3)=17, a(n) = -3*a(n-1)-8*a(n-2)-3*a(n-3)-a(n-4). - Harvey P. Dale, May 26 2011

Extensions

More terms from Jason Yuen, Aug 31 2025