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A038846
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4-fold convolution of A000302 (powers of 4); expansion of 1/(1-4*x)^4.
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17
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1, 16, 160, 1280, 8960, 57344, 344064, 1966080, 10813440, 57671680, 299892736, 1526726656, 7633633280, 37580963840, 182536110080, 876173328384, 4161823309824, 19585050869760, 91396904058880, 423311976693760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also minimal 3-covers of a labeled n-set that cover 3 points of that set uniquely (if offset is 3). Cf. A057524 for unlabeled case - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 02 2000
Also convolution of A020918 with A000984 (central binomial coefficients)
Let M=[1,0,0,i;0,1,i,0;0,i,1,0;i,0,0,1], i=sqrt(-1). Then 1/det(I-xM)=1/(1-4x)^4. - Paul Barry (pbarry(AT)wit.ie), Apr 27 2005
With a different offset, number of n-permutations (n=4)of 5 objects u, v, w, z, x with repetition allowed, containing exactly three u's. Example: a(1)=16 because we have uuuv, uuvu, uvuu, vuuu, uuuw, uuwu, uwuu, wuuu, uuuz, uuzu, uzuu, zuuu, uuux, uuxu, uxuu and xuuu - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 19 2008
From A152818. a(n)=A006044/6. [From Paul Curtz (bpcrtz(AT)free.fr), Jan 07 2009]
Also convolution of A000302 with A038845, also convolution of A002457 with A002802, also convolution of A002697. [From Rui Duarte, Oct 08 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
| a(n)=binomial(n+3, 3)*4^n; G.f. 1/(1-4*x)^4.
a(n) = sum( a+b+c+d+e+f+g+h=n, f(a)*f(b)*f(c)*f(d)*f(e)*f(f)*f(g)*f(h)) with f(n)=A000984(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 22 2004
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MAPLE
| seq(seq(binomial(i, j)*4^(i-3), j =i-3), i=3..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2007
seq(binomial(n+3, 3)*4^n, n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 19 2008
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PROG
| (Other) SAGE: [lucas_number2(n, 4, 0)*binomial(n, 3)/2^6 for n in xrange(3, 26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 11 2009]
(MAGMA) [4^n*Binomial(n+3, 3): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011
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CROSSREFS
| Cf. A000302, A020918, A000984.
Cf. A038231.
Sequence in context: A144453 A121036 A073394 * A079767 A079768 A053410
Adjacent sequences: A038843 A038844 A038845 * A038847 A038848 A038849
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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