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

0,3

Links

Table of n, a(n) for n=0..21.

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

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

Example

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.

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 *)

Crossrefs

Cf. A008464.

Sequence in context: A210158 A130611 A127747 * A125448 A163148 A355414

Adjacent sequences: A090664 A090665 A090666 * A090668 A090669 A090670

Keyword

nonn,easy

Author

Henry Bottomley, Dec 16 2003

Extensions

More terms from Colin Barker, May 15 2013

Status

approved