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

0,1

Links

Table of n, a(n) for n=0..28.

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

Formula

G.f.: (-2x^2-2x+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) [From 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

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 *)

Crossrefs

Sequence in context: A072136 A286444 A080406 * A104270 A038731 A244762

Adjacent sequences: A036679 A036680 A036681 * A036683 A036684 A036685

Keyword

nonn,easy

Author

Floor van Lamoen

Status

approved