A008464 - OEIS

A008464

a(n) = 2^(2n+3) - 2^n*(n+3).

1, 5, 24, 108, 464, 1936, 7936, 32192, 129792, 521472, 2091008, 8375296, 33525760, 134156288, 536739840, 2147205120, 8589344768, 34358493184, 137436332032, 549750308864, 2199011721216, 8796068904960, 35184321757184, 140737383497728, 562949735317504

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OFFSET

-1,2

COMMENTS

a(n-2) = 2^(2n-1) - (n+1)*2^(n-2) is number of compositions of 2n where each part <= n: e.g., for n=2, 4 can be written 5 ways with no part greater than 2 as 1+1+1+1 = 1+1+2 = 1+2+1 = 2+1+1 = 2+2. - Henry Bottomley, Feb 03 2003

LINKS

Delbert L. Johnson, Table of n, a(n) for n = -1..1659

Index entries for linear recurrences with constant coefficients, signature (8,-20,16).

FORMULA

G.f.: 8/(1-4*x) - 3/(1-2*x) - 2*x/(1-2*x)^2 + 1/x. - R. J. Mathar, Nov 21 2007

a(n) = 8*a(n-1) - 20*a(n-2) + 16*a(n-3). - Wesley Ivan Hurt, Sep 04 2022

MAPLE

A008464:=n->2^(2*n+3)-2^n*(n+3); seq(A008464(n), n=-1..22);

MATHEMATICA

Table[Coefficient[Series[(1 - x)/(1 - 2 x + x^(n + 1)), {x, 0, 2 n}], x^(2 n)], {n, 1, 22}] (* Geoffrey Critzer, May 29 2013 *)

LinearRecurrence[{8, -20, 16}, {1, 5, 24}, 30] (* Harvey P. Dale, May 15 2022 *)

PROG