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%I #27 May 13 2022 15:39:10
%S 1,91,703,2701,7381,16471,32131,56953,93961,146611,218791,314821,
%T 439453,597871,795691,1038961,1334161,1688203,2108431,2602621,3178981,
%U 3846151,4613203,5489641,6485401,7610851,8876791,10294453,11875501,13632031,15576571,17722081,20081953
%N Each term of A003215 (centered hexagonal numbers) is multiplied by the corresponding term of A003154 (centered dodecagonal numbers).
%C The digital root (A010888) of each term is 1.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = A003215(n) * A003154(n).
%F a(n) = 18*n^4 - 36*n^3 + 27*n^2 - 9*n + 1.
%e 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 x 73] = 2701.
%t LinearRecurrence[{5,-10,10,-5,1},{1,91,703,2701,7381},40] (* _Harvey P. Dale_, May 13 2022 *)
%Y Cf. A003215, A003154.
%K nonn,easy
%O 1,2
%A _David Z. Crookes_, Nov 09 2020