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

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

0,2

Comments

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

Links

Table of n, a(n) for n=0..41.

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

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A044216 A044597 A138625 * A154405 A092373 A240954

Adjacent sequences: A381193 A381194 A381195 * A381197 A381198 A381199

Keyword

nonn,easy

Author

Aaron David Fairbanks, Feb 16 2025

Status

approved