A100186 Structured heptagonal anti-diamond numbers (vertex structure 7).

1, 16, 67, 176, 365, 656, 1071, 1632, 2361, 3280, 4411, 5776, 7397, 9296, 11495, 14016, 16881, 20112, 23731, 27760, 32221, 37136, 42527, 48416, 54825, 61776, 69291, 77392, 86101, 95440, 105431, 116096

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)*(22*n^3 - 24*n^2 + 8*n).

G.f.: x*(1 + 12*x + 9*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

E.g.f.: (3*x +21*x^2 +11*x^3)*exp(x)/3. - G. C. Greubel, Nov 08 2018

Mathematica

Table[(22*n^3 - 24*n^2 + 8*n)/6, {n, 1, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 16, 67, 176}, 40] (* G. C. Greubel, Nov 08 2018 *)

Prog

(Magma) [(1/6)*(22*n^3-24*n^2+8*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(PARI) vector(40, n, (22*n^3 -24*n^2 +8*n)/6) \\ G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A063521 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers.

Sequence in context: A243956 A216306 A321180 * A344600 A271913 A178574

Adjacent sequences: A100183 A100184 A100185 * A100187 A100188 A100189

Keyword

nonn,easy

Author

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

Status

approved