A137359 a(n) = Sum_{k <= n/2 } k*binomial(n-2k, 3k).

0, 0, 0, 0, 0, 1, 4, 10, 20, 35, 58, 98, 176, 333, 640, 1213, 2242, 4052, 7226, 12835, 22842, 40788, 72952, 130344, 232200, 412190, 729466, 1288216, 2272012, 4003795, 7050358, 12404345, 21801674, 38275760, 67125420, 117604174, 205865368, 360090917, 629414866

Offset: 0

Author

Don Knuth, Apr 11 2008

Keywords

• nonn
• base

References

• D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,8,-7,6,-2,0,-1).

Crossrefs

Cf. A137356-A137361, A136444.

Programs

Maple

a:= n-> (Matrix([[10, 4, 1, 0$7]]). Matrix (10, (i,j)-> if i=j-1 then 1 elif j=1 then [6, -15, 20, -15, 8, -7, 6, -2, 0, -1][i] else 0 fi)^n)[1,8]: seq (a(n), n=0..50); # Alois P. Heinz, Oct 23 2008

Mathematica

LinearRecurrence[{6, -15, 20, -15, 8, -7, 6, -2, 0, -1}, {0, 0, 0, 0, 0, 1, 4, 10, 20, 35}, 50] (* Paolo Xausa, Mar 17 2024 *)

Formula

G.f.: x^5*(1-x)^2/(x^5+x^3-3*x^2+3*x-1)^2. - Alois P. Heinz, Oct 23 2008