A090667 Number of compositions of 3n with each part less than or equal to n.

1, 1, 13, 149, 1490, 13624, 117920, 987568, 8111200, 65866496, 531372800, 4270866688, 34254920192, 274425014272, 2197077311488, 17583865032704, 140702055981056, 1125749585477632, 9006563605151744, 72054913990721536, 576449482336632832, 4611638739487686656

Offset: 0

Author

Henry Bottomley, Dec 16 2003

Keywords

• nonn
• easy

Examples

			a(2)=13 since there is one composition of 6 of the form 1+1+1+1+1+1, five of the form 2+1+1+1+1, six of the form 2+2+1+1 and one of the form 2+2+2 and 1+5+6+1=13.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (22,-188,808,-1856,2176,-1024).

Crossrefs

Cf. A008464.

Programs

Maple

A090667:=n->`if`(n=0,1,2^(3*n-1)-(2*n+1)*2^(2*n-2)+(n+2)*(n-1)*2^(n-4)); seq(A090667(n), n=0..50); # Wesley Ivan Hurt, Nov 14 2013

Mathematica

LinearRecurrence[{22,-188,808,-1856,2176,-1024},{1,1,13,149,1490,13624,117920},30] (* Harvey P. Dale, May 04 2024 *)

Formula

a(n) = 2^(3n-1)-(2n+1)*2^(2n-2)+(n+2)*(n-1)*2^(n-4), n>0.

G.f.: (896*x^6-1968*x^5+1704*x^4-757*x^3+179*x^2-21*x+1) / ((2*x-1)^3*(4*x-1)^2*(8*x-1)). - Colin Barker, May 15 2013

Extensions

More terms from Colin Barker, May 15 2013