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A004188
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n*(3*n^2-1)/2.
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21
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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 analogue of centered polygonal numbers.
(1), (4+7), (10+13+16), (19+22+25+28), ... - Jon Perry, Sep 10 2004
a(n)=A000447+A000292 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 21 2007
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REFERENCES
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T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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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
a(n)=C(2*n+1,3)+C(n+1,3), n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 21 2007
G.f. x*(1+7*x+x^2) / (x-1)^4 . - R. J. Mathar, Oct 08 2011
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MAPLE
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seq(binomial(2*n+1, 3)+binomial(n+1, 3), n=0..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 21 2007
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MATHEMATICA
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Table[n(3n^2-1)/2, {n, 0, 80}] (* From Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
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PROG
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(PARI) vector(40, n, n*(3*n^2-1)/2)
(MAGMA) [n*(3*n^2-1)/2: n in [0..50]]; // Vincenzo Librandi, May 15 2011
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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.
Cf. A016061, A002412.
Cf. A051682.
Sequence in context: A103738 A045801 A162261 * A163634 A173373 A127867
Adjacent sequences: A004185 A004186 A004187 * A004189 A004190 A004191
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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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