A389797 Centered 27-gonal numbers.

1, 28, 82, 163, 271, 406, 568, 757, 973, 1216, 1486, 1783, 2107, 2458, 2836, 3241, 3673, 4132, 4618, 5131, 5671, 6238, 6832, 7453, 8101, 8776, 9478, 10207, 10963, 11746, 12556, 13393, 14257, 15148, 16066, 17011, 17983, 18982, 20008, 21061, 22141, 23248, 24382, 25543, 26731

Offset

1,2

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 51.

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Centered Polygonal Numbers.

Index entries for sequences related to centered polygonal numbers.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = (27*n^2 - 27*n + 2)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3.

G.f.: x*(1 + 25*x + x^2)/(1 - x)^3.

E.g.f.: exp(x)*(2 + 27*x^2)/2 - 1.

Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(19/3)*Pi/6)/(3*sqrt(57)).

Sum_{n>=1} a(n)/n! = (29*e - 2)/2.

Sum_{n>=1} (-1)*a(n)/n! = (29 - 2*e)/(2*e).

Mathematica

a[n_]:=(27n^2-27n+2)/2; Array[a, 45]

Crossrefs

Cf. centered polygonal numbers listed in A069190.

Cf. A195314, A389798, A389799.

Sequence in context: A039415 A043238 A044018 * A124783 A126382 A165009

Adjacent sequences: A389794 A389795 A389796 * A389798 A389799 A389800

Keyword

nonn,easy

Author

Stefano Spezia, Oct 15 2025

Status

approved