A036682 T(n+3,3) with T as in A036355.

3, 10, 32, 84, 207, 478, 1060, 2272, 4744, 9692, 19446, 38420, 74909, 144378, 275464, 520864, 977005, 1819426, 3366182, 6191056, 11325040, 20613800, 37350060, 67389320, 121113335, 216877274, 387048080, 688559356, 1221323947

Offset: 0

Author

Floor van Lamoen

Keywords

• nonn
• easy
• changed

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-2,-8,5,8,-2,-4,-1).

Crossrefs

Cf. A036355, A001872, A001628.

Programs

Mathematica

CoefficientList[Series[(-2x^2-2x+3)/(1-x-x^2)^4,{x,0,30}],x] (* or *) LinearRecurrence[{4,-2,-8,5,8,-2,-4,-1},{3,10,32,84,207,478,1060,2272},30] (* Harvey P. Dale, May 06 2012 *)

Formula

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

a(0)=3, a(1)=10, a(2)=32, a(3)=84, a(4)=207, a(5)=478, a(6)=1060, a(7)=2272, a(n) = 4*a(n-1)-2*a(n-2)-8*a(n-3)+5*a(n-4)+8*a(n-5)-2*a(n-6)-4*a(n-7)-a(n-8). - Harvey P. Dale, May 06 2012

a(n) = 3*A001872(n)-2*A001872(n-1)-2*A001872(n-2) = A001872(n)+2*A001628(n). - R. J. Mathar, Jul 03 2022