A381196 - OEIS

%I #36 Mar 05 2025 20:44:00

%S 1,29,97,205,353,541,769,1037,1345,1693,2081,2509,2977,3485,4033,4621,

%T 5249,5917,6625,7373,8161,8989,9857,10765,11713,12701,13729,14797,

%U 15905,17053,18241,19469,20737,22045,23393,24781,26209,27677,29185,30733,32321,33949

%N Stellated octagon numbers: a(n) = 20*n^2 + 8*n + 1.

%C Sequence found by reading the line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. - _Omar E. Pol_, Feb 17 2025

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = (4*n + 1)^2 + 4*n^2.

%F a(n) = A001844(3*n - 2) + 4*A000217(n - 1).

%F a(n) = 4 * A168668(n) + 1.

%F a(n) = A016814(n) + A016742(n).

%F G.f.: (13*x^2+26*x+1) / (1-x)^3.

%F E.g.f.: exp(x) * (1 + 28*x + 20*x^2). - _Stefano Spezia_, Feb 23 2025

%e Illustration of initial terms:

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%e .   1          29                     97

%t a[n_] := 20*n^2 + 8*n + 1; Array[a, 42, 0] (* _Amiram Eldar_, Feb 17 2025 *)

%Y Cf. A000217, A001844, A016742, A016814, A168668, A195162.

%K nonn,easy

%O 0,2

%A _Aaron David Fairbanks_, Feb 16 2025