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A140229
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Binomial transform of [1, 3, 3, 1, -2, 3, -4, 5, ...].
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2
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1, 4, 10, 20, 33, 49, 68, 90, 115, 143, 174, 208, 245, 285, 328, 374, 423, 475, 530, 588, 649, 713, 780, 850, 923, 999, 1078, 1160, 1245, 1333, 1424, 1518, 1615, 1715, 1818, 1924, 2033, 2145, 2260, 2378, 2499, 2623, 2750, 2880, 3013, 3149, 3288, 3430, 3575
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OFFSET
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1,2
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COMMENTS
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The falling diagonal starting with T(1,4) in A049777 (as a square array) gives the terms of this sequence for n >=3. - Bob Selcoe, Oct 27 2014
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LINKS
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FORMULA
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A007318 * [1, 3, 3, 1, -2, 3, -4, 5,...].
G.f.: x(1+x+x^2+x^3-x^4)/(1-x)^3. a(n) = 3*a(n-1) -3*a(n-2) + a(n-3), n>5. a(n+1)-a(n) = A016777(n), n>3. - R. J. Mathar, Nov 25 2008
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EXAMPLE
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a(5) = 33 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, -2) = (1 + 12 + 18 + 4 - 2).
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MAPLE
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1, 4, seq((1/2)*(n+1)*(3*n-4), n=3..40); # Emeric Deutsch, May 18 2008
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MATHEMATICA
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PROG
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(Magma) [1, 4] cat [(n+1)*(3*n-4)/2: n in [3..50]]; // Vincenzo Librandi, Oct 27 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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