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A100186
Structured heptagonal anti-diamond numbers (vertex structure 7).
3
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
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
KEYWORD
nonn,easy
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved