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A100189
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Equatorial structured meta-anti-diamond numbers, the n-th number from an equatorial structured n-gonal anti-diamond number sequence.
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3
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1, 6, 27, 92, 245, 546, 1071, 1912, 3177, 4990, 7491, 10836, 15197, 20762, 27735, 36336, 46801, 59382, 74347, 91980, 112581, 136466, 163967, 195432, 231225, 271726, 317331, 368452, 425517, 488970, 559271, 636896
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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FORMULA
| a(n) = (1/6)*(4*n^4-12*n^3+20*n^2-6*n).
a(1)=1, a(2)=6, a(3)=27, a(4)=92, a(5)=245, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, July 05 2011
G.f.: x*(1+x)*(1+7*x^2)/(1-x)^5. - Colin Barker, Jan 19 2012
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EXAMPLE
| There are no 1- or 2-gonal anti-diamonds, so 1 and (2n+2) are used as the first and second terms since all the sequences begin as such.
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MATHEMATICA
| Table[(4n^4-12n^3+20n^2-6n)/6, {n, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 6, 27, 92, 245}, 40] "(* From Harvey P. Dale, July 05 2011 *)"
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PROG
| (MAGMA) [(1/6)*(4*n^4-12*n^3+20*n^2-6*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
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CROSSREFS
| Cf. A000578, A096000, A051673, A005915, A100186, A100187 - "equatorial" structured anti-diamonds; A100188 - "polar" structured meta-anti-diamond numbers; A006484 for other structured meta numbers; and A100145 for more on structured numbers.
Sequence in context: A100188 A131985 A125196 * A052267 A038166 A121596
Adjacent sequences: A100186 A100187 A100188 * A100190 A100191 A100192
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KEYWORD
| nonn,easy
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AUTHOR
| James A. Record (james.record(AT)gmail.com), Nov 07 2004
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