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A037235
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a(n) = n*(2*n^2 - 3*n + 4)/3.
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5
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0, 1, 4, 13, 32, 65, 116, 189, 288, 417, 580, 781, 1024, 1313, 1652, 2045, 2496, 3009, 3588, 4237, 4960, 5761, 6644, 7613, 8672, 9825, 11076, 12429, 13888, 15457, 17140, 18941, 20864, 22913, 25092, 27405, 29856, 32449, 35188, 38077, 41120, 44321, 47684, 51213
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OFFSET
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0,3
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COMMENTS
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Row sums of triangle A134249. Also, binomial transform of (1, 3, 6, 4, 0, 0, 0, ...). - Gary W. Adamson, Oct 15 2007
Binomial transform of a(n) starts: 0, 1, 6, 28, 112, 400, 1312, 4032, ... . - Wesley Ivan Hurt, Oct 21 2014
Number of equivalence classes of n-tuples from the set {1,0,-1} where at the number of nonzero elements is 1,2, or 3 and two n-tuples are equivalent if they are negatives of each other. - Michael Somos, Oct 19 2022
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LINKS
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FORMULA
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G.f.: x*(1+3*x^2)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=4, a(3)=13. - Yosu Yurramendi, Sep 03 2013
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MAPLE
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MATHEMATICA
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PROG
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(R)
a <- c(0, 1, 4, 13)
for(n in (length(a)+1):30) a[n] <- 4*a[n-1] -6*a[n-2] +4*a[n-3] -a[n-4]
a
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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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