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Search: id:A004126
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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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COMMENT
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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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FORMULA
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Partial sums of A069099, centered heptagonal numbers (A000566). - Jonathan Vos Post (jvospost3(AT)gmail.com), 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
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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
a:=n->sum((n+j)^2-(n+j), j=1..n): seq(a(n)/2, n=0..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2008
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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: A054310 A072887 A133739 this_sequence A118444 A048374 A140323
Adjacent sequences: A004123 A004124 A004125 this_sequence A004127 A004128 A004129
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KEYWORD
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nonn
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AUTHOR
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Albert D. Rich (Albert_Rich(AT)msn.com).
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