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A027914
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T(n,0) + T(n,1) + ... + T(n,n), T given by A027907.
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13
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1, 2, 6, 17, 50, 147, 435, 1290, 3834, 11411, 34001, 101400, 302615, 903632, 2699598, 8068257, 24121674, 72137547, 215786649, 645629160, 1932081885, 5782851966, 17311097568, 51828203475, 155188936431, 464732722872
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OFFSET
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0,2
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COMMENTS
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Let b(n)=a(n) mod 2; then b(n)=1/2+(-1)^n*(1/2-A010060(floor(n/2))) - Benoit Cloitre, Mar 23 2004
Binomial transform of A027306 . Inverse binomial transform of = A032443 . Hankel transform is {1, 2, 3, 4, ..., n, ...} . - Philippe DELEHAM, Jul 20 2005
Sums of rows of the triangle in A111808. - Reinhard Zumkeller, Aug 17 2005
Number of 3-ary words of length n in which the number of 1's does not exceed the number of 0's. - David Scambler, Aug 14 2012
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = ( 3^n + A002426(n) )/2; lim n -> infinity a(n+1)/a(n) = 3; 3^n < 2*a(n) < 3^(n+1) - Benoit Cloitre, Sep 28 2002
a(n)= (1/2) *(sum(k=0, n, binomial(n, k)*binomial(n-k, k))+3^n); a(n)=sum(k=0, n, sum(i=0, k, binomial(n, i)*binomial(n-i, k))); a(n)=3^n/2*(1+c/sqrt(n)+0(n^-1/2)) where c=0.5... - Benoit Cloitre, Jan 26 2003
a(n)=n!*sum(i+j+k=n, 1/(i!*j!*k!)) 0<=i<=n, 0<=k<=j<=n - Benoit Cloitre, Mar 23 2004
G.f.: (1+x+sqrt(1-2x-3x^2))/(2(1-2x-3x^2)); a(n)=sum{k=0..n, floor((k+2)/2)*sum{i=0..floor((n-k)/2), C(n, i)C(n-i, i+k)((k+1)/(i+k+1))}}; - Paul Barry, Sep 23 2005; corrected Jan 20 2008
Conjecture: n*a(n) +(-5*n+4)*a(n-1) +3*(n-2)*a(n-2) +9*(n-2)*a(n-3)=0. - R. J. Mathar, Dec 02 2012
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PROG
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(PARI) a(n)=sum(i=0, n, polcoeff((1+x+x^2)^n, i, x))
(PARI) a(n)=sum(i=0, n, sum(j=0, n, sum(k=0, j, if(i+j+k-n, 0, (n!/i!/j!/k!)))))
(Haskell)
a027914 n = sum $ take (n + 1) $ a027907_row n
-- Reinhard Zumkeller, Jan 22 2013
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CROSSREFS
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Cf. A025191, A027915, A081673.
Cf. A092255.
Cf. A055217.
Sequence in context: A148445 A148446 A173993 * A098703 A025272 A148447
Adjacent sequences: A027911 A027912 A027913 * A027915 A027916 A027917
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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