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A137221 a(n) = 5*a(n-1) - 9*a(n-2) + 8*a(n-3) - 4*a(n-4). 1
0, 0, 0, 1, 5, 16, 43, 107, 256, 597, 1365, 3072, 6827, 15019, 32768, 70997, 152917, 327680, 699051, 1485483, 3145728, 6640981, 13981013, 29360128, 61516459, 128625323, 268435456, 559240533, 1163220309, 2415919104, 5010795179 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (5, -9, 8, -4).

FORMULA

Binomial transform of A002264; a(n+1)-2a(n)=A024495.

O.g.f.: x^3/{(x^2-x+1)(-1+2*x)^2} . a(n)=[ -3*2^n+A001787(n+1)+2*A010892(n)]/6. - R. J. Mathar, Mar 17 2008

a(n) = (1/6)*{1/2-(1/2)*I*sqrt(3)}^n+(1/6)*{1/2+(1/2)*I*sqrt(3)}^n-(1/3)*2^n+[(1/18)*I]*{1/2-(1 /2)*I*sqrt(3)}^n*sqrt(3)+(1/6)*2^n*n-[(1/18)*I]*{1/2+(1/2)*I*sqrt(3)}^n*sqrt(3), with n>=0 and I=sqrt(-1). - Paolo P. Lava, Jun 09 2008

CROSSREFS

Recurrence in A100335, essentially a(n) differences.

Sequence in context: A034358 A036888 A053221 * A137234 A271359 A299810

Adjacent sequences:  A137218 A137219 A137220 * A137222 A137223 A137224

KEYWORD

nonn

AUTHOR

Paul Curtz, Mar 07 2008

EXTENSIONS

More terms from R. J. Mathar, Mar 17 2008

STATUS

approved

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Last modified October 21 14:48 EDT 2019. Contains 328301 sequences. (Running on oeis4.)