

A100189


Equatorial structured metaantidiamond numbers, the nth number from an equatorial structured ngonal antidiamond number sequence.


3



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
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OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5, 10, 10, 5, 1).


FORMULA

a(n) = (1/6)*(4*n^412*n^3+20*n^26*n).
a(1)=1, a(2)=6, a(3)=27, a(4)=92, a(5)=245, a(n)=5*a(n1)10*a(n2)+ 10*a(n3)5*a(n4)+a(n5).  Harvey P. Dale, Jul 05 2011
G.f.: x*(1+x)*(1+7*x^2)/(1x)^5.  Colin Barker, Jan 19 2012


EXAMPLE

There are no 1 or 2gonal antidiamonds, so 1 and (2n+2) are used as the first and second terms since all the sequences begin as such.


MATHEMATICA

Table[(4n^412n^3+20n^26n)/6, {n, 40}] (* or *) LinearRecurrence[ {5, 10, 10, 5, 1}, {1, 6, 27, 92, 245}, 40] (* Harvey P. Dale, Jul 05 2011 *)


PROG

(MAGMA) [(1/6)*(4*n^412*n^3+20*n^26*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011


CROSSREFS

Cf. A000578, A096000, A051673, A005915, A100186, A100187  "equatorial" structured antidiamonds; A100188  "polar" structured metaantidiamond numbers; A006484 for other structured meta numbers; and A100145 for more on structured numbers.
Sequence in context: A100188 A131985 A125196 * A052267 A038166 A327384
Adjacent sequences: A100186 A100187 A100188 * A100190 A100191 A100192


KEYWORD

nonn,easy


AUTHOR

James A. Record (james.record(AT)gmail.com), Nov 07 2004


STATUS

approved



