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

Author

David Z Crookes, Nov 09 2020

Keywords

• nonn
• easy
• changed

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A003154, A003215, A010888.

Programs

Mathematica

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

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)