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A105163
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a(n) = (n^3 - 7*n + 12)/6.
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13
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1, 1, 3, 8, 17, 31, 51, 78, 113, 157, 211, 276, 353, 443, 547, 666, 801, 953, 1123, 1312, 1521, 1751, 2003, 2278, 2577, 2901, 3251, 3628, 4033, 4467, 4931, 5426, 5953, 6513, 7107, 7736, 8401, 9103, 9843, 10622, 11441, 12301, 13203, 14148, 15137, 16171
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OFFSET
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1,3
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COMMENTS
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A floretion-generated sequence relating to the sequence "A class of Boolean functions of n variables and rank 2" (among several others- see link "Sequences in Context").
a(n) is the number of P-position in 2-modular Nim with n-1 piles. - Tanya Khovanova and Karan Sarkar, Jan 10 2016
a(n) is the number of parking functions of size n-1 avoiding the patterns 123 and 231. - Lara Pudwell, Apr 10 2023
a(n) is the number of length (n-2) strings on the alphabet {0,1,2} with digit sum at most 3. - Daniel T. Martin, May 23 2023
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LINKS
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FORMULA
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Sequence starting (1, 3, 8, 17, ...) = binomial transform of [1, 2, 3, 1, 0, 0, 0, ...]. - Gary W. Adamson, Apr 24 2008
G.f.: x*(1 - 3*x + 5*x^2 - 2*x^3)/(1 - x)^4. - Colin Barker, Mar 26 2012
a(n) = 2*a(n-1) - a(n-2) + n - 1, for all n in Z. - Gionata Neri, Jul 28 2016
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MAPLE
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MATHEMATICA
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Rest@ CoefficientList[Series[x (1 - 3 x + 5 x^2 - 2 x^3)/(1 - x)^4, {x, 0, 46}], x] (* or *)
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PROG
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(Python) for n in range(1, 45): print((n**3 - 7*n + 12)/6, end=', ') # Stefano Spezia, Jan 05 2019
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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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