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0, 1, 12, 43, 104, 205, 356, 567, 848, 1209, 1660, 2211, 2872, 3653, 4564, 5615, 6816, 8177, 9708, 11419, 13320, 15421, 17732, 20263, 23024, 26025, 29276, 32787, 36568, 40629, 44980, 49631, 54592
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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.
Also as a(n)=(1/6)*(10*n^3-4*n), n>0: structured pentagonal anti-diamond numbers (vertex structure 11) (Cf. A051673 = alternate vertex A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov. 7, 2004.
a(n+1)-10*a(n)=(n+1)*(5*(n+1)^2-2)/3 - (10n(n+1)(n+2)/6)=n. The unit digits are 0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9... - Eric Desbiaux, Aug 18 2008
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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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G.f.: x*(1+8*x+x^2)/(1-x)^4. [Colin Barker, Jan 08 2012]
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MATHEMATICA
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Table[n(5n^2-2)/3, {n, 0, 80}] (* From Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
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PROG
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(MAGMA) [n*(5*n^2-2)/3: 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.
Sequence in context: A125221 A082829 A003357 * A062749 A004636 A136279
Adjacent sequences: A004463 A004464 A004465 * A004467 A004468 A004469
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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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