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A081139 9th binomial transform of (0,0,1,0,0,0,...). 13
0, 0, 1, 27, 486, 7290, 98415, 1240029, 14880348, 172186884, 1937102445, 21308126895, 230127770466, 2447722649502, 25701087819771, 266895911974545, 2745215094595320, 28001193964872264, 283512088894331673 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Starting at 1, the three-fold convolution of A001019 (powers of 9).

Number of n-permutations (n=3)of 10 objects p, q, r, s, u, v, w, z, x, y with repetition allowed, containing exactly two u's. - Zerinvary Lajos, May 23 2008

Number of n-permutations (n=3) of 10 objects p, r, q, s, u, v, w, z, x, y with repetition allowed, containing exactly two u's. Example: a(3)=27 because we have uup, uur, uuq, uus, uuw, uuv, uuz, uux, uuy, upu, uru, uqu, usu, uwu, uvu, uzu, uxu, uyu, puu, ruu, quu, suu, wuu, vuu, zuu, xuu, yuu. - Zerinvary Lajos, Jun 12 2008, Jul 10 2008

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (27,-243,729).

FORMULA

a(n) = 27a(n-1) - 243a(n-2) + 729a(n-3), a(0)=a(1)=0, a(2)=1.

a(n) = 9^(n-2)*binomial(n, 2).

G.f.: x^2/(1-9x)^3.

MAPLE

seq(binomial(n+2, 2)*9^n, n=-2..16); # Zerinvary Lajos, May 23 2008

MATHEMATICA

LinearRecurrence[{27, -243, 729}, {0, 0, 1}, 30] (* Harvey P. Dale, Jan 30 2018 *)

PROG

(Sage)[lucas_number2(n, 9, 0)*binomial(n, 2)/9^2 for n in xrange(0, 20)] # Zerinvary Lajos, Mar 13 2009

(MAGMA) [9^n* Binomial(n+2, 2): n in [-2..20]]; // Vincenzo Librandi, Oct 16 2011

CROSSREFS

Cf. A081138, A081140.

Sequence in context: A026006 A024346 A025983 * A020976 A024114 A025982

Adjacent sequences:  A081136 A081137 A081138 * A081140 A081141 A081142

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 08 2003

STATUS

approved

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)