A389798 Centered 29-gonal numbers.

1, 30, 88, 175, 291, 436, 610, 813, 1045, 1306, 1596, 1915, 2263, 2640, 3046, 3481, 3945, 4438, 4960, 5511, 6091, 6700, 7338, 8005, 8701, 9426, 10180, 10963, 11775, 12616, 13486, 14385, 15313, 16270, 17256, 18271, 19315, 20388, 21490, 22621, 23781, 24970, 26188, 27435, 28711

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) = (29*n^2 - 29*n + 2)/2.

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

G.f.: x*(1 + 27*x + x^2)/(1 - x)^3.

E.g.f.: exp(x)*(2 + 29*x^2)/2 - 1.

Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(21/29)*Pi/2)/sqrt(609).

Sum_{n>=1} a(n)/n! = (31*e - 2)/2.

Sum_{n>=1} (-1)*a(n)/n! = (31 - 2*e)/(2*e).

Mathematica

a[n_]:=(29n^2-29n+2)/2; Array[a, 45]

Crossrefs

Cf. centered polygonal numbers listed in A069190.

Cf. A195314, A389797, A389799.

Sequence in context: A058903 A254474 A103906 * A124799 A126384 A025417

Adjacent sequences: A389795 A389796 A389797 * A389799 A389800 A389801

Keyword

nonn,easy

Author

Stefano Spezia, Oct 15 2025

Status

approved