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A090667 Number of compositions of 3n with each part less than or equal to n. 1
1, 1, 13, 149, 1490, 13624, 117920, 987568, 8111200, 65866496, 531372800, 4270866688, 34254920192, 274425014272, 2197077311488, 17583865032704, 140702055981056, 1125749585477632, 9006563605151744, 72054913990721536, 576449482336632832, 4611638739487686656 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Cf. A008464.

Sequence in context: A210158 A130611 A127747 * A125448 A163148 A185405

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

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Last modified February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)