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A055991
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a(n) is its own 4th difference.
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9
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1, 5, 19, 69, 250, 907, 3292, 11949, 43371, 157422, 571388, 2073943, 7527704, 27322992, 99173120, 359964521, 1306548149, 4742323107, 17213011605, 62477347458, 226771411939, 823102698260, 2987581397893, 10843899100203
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of distinct matrix products in (A+B+C+D+E)^n where A,B,C and D all commute with each other, but not with E. - Paul D. Hanna and Max Alekseyev, Feb 01 2006
Row sums of Riordan array (1,1/(1-x)^4). - Paul Barry, Feb 02 2006
Equals the INVERT transform of the tetrahedral series.
a(4) = 69 = (1, 4, 10) dot (19, 5, 1) + 20; = (19 + 20 + 10) + 20. (End)
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LINKS
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FORMULA
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Letting a(0)=1, we have a(n)=sum(u=0, n-1, sum(v=0, u, sum(w=0, v, sum(x=0, w, a(x))))) for n>0. - Benoit Cloitre, Jan 26 2003
a(n) = sum{k=0..n, binomial(4n-3k-1,k)}. - Paul Barry, Feb 02 2006
G.f.: x/(1-5x+6x^2-4x^3+x^4). - Paul Barry, Feb 02 2006
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MATHEMATICA
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LinearRecurrence[{5, -6, 4, -1}, {1, 5, 19, 69}, 30] (* Harvey P. Dale, Feb 27 2013 *)
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PROG
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(Magma) I:=[1, 5, 19, 69]; [n le 4 select I[n] else 5*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 05 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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