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A081138 8th binomial transform of (0,0,1,0,0,0,...). 10
0, 0, 1, 24, 384, 5120, 61440, 688128, 7340032, 75497472, 754974720, 7381975040, 70866960384, 670014898176, 6253472382976, 57724360458240, 527765581332480, 4785074604081152, 43065671436730368, 385057768140177408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Starting at 1, the three-fold convolution of A001018 (powers of 8).

Number of n-permutations (n=3) of 9 objects p, r, q, u, v, w, z, x, y with repetition allowed, containing exactly two u's. Example: a(3)=24 because we have uup, uur, uuq, uuw, uuv, uuz, uux, uuy, upu, uru, uqu, uwu, uvu, uzu, uxu, uyu, puu, ruu, quu, wuu, vuu, zuu, xuu, yuu. - Zerinvary Lajos, Jun 12 2008

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (24,-192,512).

FORMULA

a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3) for n>2, a(0)=a(1)=0, a(2)=1.

a(n) = 8^(n-2)*binomial(n, 2).

G.f.: x^2/(1 - 8*x)^3.

MAPLE

seq(binomial(n+2, 2)*8^n, n=-2..18); # Zerinvary Lajos, Jun 12 2008

MATHEMATICA

LinearRecurrence[{24, -192, 512}, {0, 0, 1}, 30] (* Harvey P. Dale, Jun 08 2014 *)

PROG

(Sage)[lucas_number2(n, 8, 0)*binomial(n, 2)/8^2 for n in xrange(0, 20)] # Zerinvary Lajos, Mar 13 2009

(MAGMA) [8^n*Binomial(n+2, 2): n in [-2..20]]; // Vincenzo Librandi, Oct 16 2011

CROSSREFS

Cf. A027474, A081139.

Sequence in context: A059157 A228406 A087292 * A269181 A266185 A114631

Adjacent sequences:  A081135 A081136 A081137 * A081139 A081140 A081141

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 08 2003

STATUS

approved

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)