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A036216
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Expansion of 1/(1-3*x)^4; 4-fold convolution of A000244 (powers of 3).
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14
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1, 12, 90, 540, 2835, 13608, 61236, 262440, 1082565, 4330260, 16888014, 64481508, 241805655, 892820880, 3252418920, 11708708112, 41712272649, 147219785820, 515269250370, 1789882659180, 6175095174171, 21171754882872
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OFFSET
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0,2
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COMMENTS
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a(n)=A027465(n+4,4) (O. Gerard's triangle).
With three leading zeros, 3rd binomial transform of (0,0,0,1,0,0,0,0,...) - Paul Barry, Mar 07 2003
Number of n-permutations (n=4) of 4 objects u, v, w, z, with repetition allowed, containing exactly three u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 23 2008
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..400
Eric Weisstein's World of Mathematics, Idempotent Number.
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FORMULA
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a(n) = 3^n*binomial(n+3, 3); g.f. 1/(1-3*x)^4.
With three leading zeros, a(n)=12a(n-1)-54a(n-2)+108a(n-3)-81a(n-4), a(0)=a(1)=a(2)=0, a(3)=1. - Paul Barry, Mar 07 2003
With three leading zeros, C(n, 3)3^(n-3)=the second binomial transform of C(n, 3). - Paul Barry, Jul 24 2003
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MAPLE
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[seq (binomial(n, 3)*3^(n-3), n=3..24)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 21 2006
seq(seq(binomial(i, j)*3^(i-3), j =i-3), i=3..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2007
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PROG
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(Sage) [lucas_number2(n, 3, 0)*binomial(n, 3)/27 for n in xrange(3, 25)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
(MAGMA) [3^n* Binomial(n+3, 3): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011
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CROSSREFS
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Cf. A000244, A027465.
Sequence in context: A130072 A135158 A073382 * A022640 A090749 A130592
Adjacent sequences: A036213 A036214 A036215 * A036217 A036218 A036219
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang
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STATUS
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approved
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