A168668 -id:A168668 - cp's OEIS frontend

1, 29, 97, 205, 353, 541, 769, 1037, 1345, 1693, 2081, 2509, 2977, 3485, 4033, 4621, 5249, 5917, 6625, 7373, 8161, 8989, 9857, 10765, 11713, 12701, 13729, 14797, 15905, 17053, 18241, 19469, 20737, 22045, 23393, 24781, 26209, 27677, 29185, 30733, 32321, 33949

Offset: 0

Aaron David Fairbanks, Feb 16 2025

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

			Illustration of initial terms:
.
.                                     o
.                                   o o o
.                             o o o o o o o o o
.              o              o o o o o o o o o
.          o o o o o          o o o o o o o o o
.          o o o o o        o o o o o o o o o o o
.   o    o o o o o o o    o o o o o o o o o o o o o
.          o o o o o        o o o o o o o o o o o
.          o o o o o          o o o o o o o o o
.              o              o o o o o o o o o
.                             o o o o o o o o o
.                                   o o o
.                                     o
.
.   1          29                     97

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

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

a(n) = (4*n + 1)^2 + 4*n^2.
a(n) = A001844(3*n - 2) + 4*A000217(n - 1).
a(n) = 4 * A168668(n) + 1.
a(n) = A016814(n) + A016742(n).
G.f.: (13*x^2+26*x+1) / (1-x)^3.
E.g.f.: exp(x) * (1 + 28*x + 20*x^2). - Stefano Spezia, Feb 23 2025

cp's OEIS Frontend

A381196 Stellated octagon numbers: a(n) = 20n^2 + 8n + 1.

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