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A004126
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n*(7*n^2-1)/6.
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18
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0, 1, 9, 31, 74, 145, 251, 399, 596, 849, 1165, 1551, 2014, 2561, 3199, 3935, 4776, 5729, 6801, 7999, 9330, 10801, 12419, 14191, 16124, 18225, 20501, 22959, 25606, 28449, 31495, 34751, 38224, 41921, 45849, 50015, 54426, 59089, 64011
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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.
Sum of n triangular numbers starting from T(n). E.g. a(4)= T(4) +T(5) +T(6) +T(7) = 10+15+21+28 = 74. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 16 2004
Also as a(n)=(1/6)*(7*n^3-n), n>0: structured heptagonal diamond numbers (vertex structure 8) (Cf. A100179 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov. 7, 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
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FORMULA
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Partial sums of A069099, centered heptagonal numbers (A000566). - Jonathan Vos Post, Mar 16 2006
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+5*x+x^2)/(1-x)^4. [Colin Barker, Mar 02 2012]
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MAPLE
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seq(binomial(2*n+1, 3)-binomial(n+1, 3), n=0..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 21 2007
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MATHEMATICA
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Table[n(7n^2-1)/6, {n, 0, 80}] (* From Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
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PROG
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(MAGMA) [n*(7*n^2-1)/6: n in [0..50]]; // Vincenzo Librandi, May 15 2011
(Maxima) A004126(n):=n*(7*n^2-1)/6$ makelist(A004126(n), n, 0, 30); /* Martin Ettl, Jan 08 2013 */
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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. A000217, A000566, A016993, A069099.
Cf. A000447, A000292.
Sequence in context: A072887 A133739 A168297 * A177342 A224000 A118444
Adjacent sequences: A004123 A004124 A004125 * A004127 A004128 A004129
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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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