A389799 Centered 30-gonal numbers.

1, 31, 91, 181, 301, 451, 631, 841, 1081, 1351, 1651, 1981, 2341, 2731, 3151, 3601, 4081, 4591, 5131, 5701, 6301, 6931, 7591, 8281, 9001, 9751, 10531, 11341, 12181, 13051, 13951, 14881, 15841, 16831, 17851, 18901, 19981, 21091, 22231, 23401, 24601, 25831, 27091, 28381, 29701

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) = 15*n^2 - 15*n + 1.

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

G.f.: x*(1 + 28*x + x^2)/(1 - x)^3.

E.g.f.: exp(x)*(1 + 15*x^2) - 1.

Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(11/15)*Pi/2)/sqrt(165).

Sum_{n>=1} a(n)/n! = 16*e - 1.

Sum_{n>=1} (-1)*a(n)/n! = (16 - e)/e.

Mathematica

a[n_]:=15n^2-15n+1; Array[a, 45]

Crossrefs

Cf. centered polygonal numbers listed in A069190.

Cf. A195314, A389797, A389798.

Sequence in context: A093758 A359650 A360488 * A139700 A124803 A126385

Adjacent sequences: A389796 A389797 A389798 * A389800 A389801 A389802

Keyword

nonn,easy

Author

Stefano Spezia, Oct 15 2025

Status

approved