A100187 Structured octagonal anti-diamond numbers (vertex structure 7).

1, 18, 77, 204, 425, 766, 1253, 1912, 2769, 3850, 5181, 6788, 8697, 10934, 13525, 16496, 19873, 23682, 27949, 32700, 37961, 43758, 50117, 57064, 64625, 72826, 81693, 91252, 101529, 112550, 124341, 136928

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Formula

a(n) = (1/6)*(26*n^3 - 30*n^2 + 10*n).

G.f.: x*(1 + 14*x + 11*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=18, a(3)=77, a(4)=204. - Harvey P. Dale, Dec 24 2012

E.g.f.: (3*x + 24*x^2 + 13*x^3)*exp(x)/3. - G. C. Greubel, Nov 08 2018

Mathematica

Table[(26n^3-30n^2+10n)/6, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 18, 77, 204}, 40] (* Harvey P. Dale, Dec 24 2012 *)

Prog

(Magma) [(1/6)*(26*n^3-30*n^2+10*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(PARI) vector(40, n, (13*n^3 -15*n^2 +5*n)/3) \\ G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A063523 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers.

Sequence in context: A296363 A164603 A229714 * A197886 A039453 A342560

Adjacent sequences: A100184 A100185 A100186 * A100188 A100189 A100190

Keyword

nonn,easy

Author

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

Status

approved