A338795 Each term of A003215 (centered hexagonal numbers) is multiplied by the corresponding term of A003154 (centered dodecagonal numbers).

1, 91, 703, 2701, 7381, 16471, 32131, 56953, 93961, 146611, 218791, 314821, 439453, 597871, 795691, 1038961, 1334161, 1688203, 2108431, 2602621, 3178981, 3846151, 4613203, 5489641, 6485401, 7610851, 8876791, 10294453, 11875501, 13632031, 15576571, 17722081, 20081953

Offset

1,2

Comments

The digital root (A010888) of each term is 1.

Links

Table of n, a(n) for n=1..33.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = A003215(n)*A003154(n).

a(n) = 18*n^4 - 36*n^3 + 27*n^2 - 9*n + 1.

From Elmo R. Oliveira, Sep 01 2025: (Start)

G.f.: -x*(1 + 86*x + 258*x^2 + 86*x^3 + x^4)/(x - 1)^5.

E.g.f.: -1 + exp(x)*(1 + 45*x^2 + 72*x^3 + 18*x^4).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5. (End)

Example

The centered hexagonal number of 4 is 37, and the centered dodecagonal number of 4 is 73, so the fourth term of the series is 37*73 = 2701.

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 91, 703, 2701, 7381}, 40] (* Harvey P. Dale, May 13 2022 *)

Crossrefs

Cf. A003154, A003215, A010888.

Sequence in context: A165220 A020218 A217841 * A084319 A047696 A043459

Adjacent sequences: A338792 A338793 A338794 * A338796 A338797 A338798

Keyword

nonn,easy

Author

David Z Crookes, Nov 09 2020

Status

approved