A100189 Equatorial structured meta-anti-diamond numbers, the n-th number from an equatorial structured n-gonal anti-diamond number sequence.

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

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^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, Jul 05 2011

G.f.: x*(1+x)*(1+7*x^2)/(1-x)^5. - Colin Barker, Jan 19 2012

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.

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] (* Harvey P. Dale, Jul 05 2011 *)

Prog

(Magma) [(1/6)*(4*n^4-12*n^3+20*n^2-6*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011

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 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