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A004188
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a(n) = n*(3*n^2 - 1)/2.
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25
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0, 1, 11, 39, 94, 185, 321, 511, 764, 1089, 1495, 1991, 2586, 3289, 4109, 5055, 6136, 7361, 8739, 10279, 11990, 13881, 15961, 18239, 20724, 23425, 26351, 29511, 32914, 36569, 40485, 44671, 49136, 53889, 58939, 64295, 69966, 75961
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OFFSET
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0,3
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COMMENTS
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3-dimensional analog of centered polygonal numbers.
(1), (4+7), (10+13+16), (19+22+25+28), ... - Jon Perry, Sep 10 2004
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REFERENCES
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E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 140.
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
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LINKS
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FORMULA
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Partial sums of n-1 3-spaced triangular numbers, e.g., a(4) = t(1) + t(4) + t(7) = 1 + 10 + 28 = 39. - Jon Perry, Jul 23 2003
E.g.f.: (x/2)*(2 + 9*x + 3*x^2)*exp(x). - G. C. Greubel, Sep 01 2017
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MAPLE
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seq(binomial(2*n+1, 3)+binomial(n+1, 3), n=0..37); # Zerinvary Lajos, Jan 21 2007
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {0, 1, 11, 39}, 40] (* Harvey P. Dale, Jul 19 2019 *)
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PROG
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(PARI) vector(40, n, n*(3*n^2-1)/2)
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CROSSREFS
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1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.
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KEYWORD
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nonn,easy
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AUTHOR
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Albert D. Rich (Albert_Rich(AT)msn.com)
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STATUS
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approved
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