A389615 a(n) = 7*n^2/2 + 3*n/2 + 1.

1, 6, 18, 37, 63, 96, 136, 183, 237, 298, 366, 441, 523, 612, 708, 811, 921, 1038, 1162, 1293, 1431, 1576, 1728, 1887, 2053, 2226, 2406, 2593, 2787, 2988, 3196, 3411, 3633, 3862, 4098, 4341, 4591, 4848, 5112, 5383, 5661, 5946, 6238, 6537, 6843, 7156, 7476, 7803, 8137, 8478, 8826, 9181, 9543, 9912, 10288, 10671, 11061, 11458

Offset

0,2

Comments

Suggested in A140065.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

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

Formula

From Stefano Spezia, Nov 02 2025: (Start)

G.f.: (1 + 3*x + 3*x^2)/(1 - x)^3.

E.g.f.: exp(x)*(2 + 10*x + 7*x^2)/2. (End)

Mathematica

A389615[n_] := n*(7*n + 3)/2 + 1; Array[A389615, 60, 0] (* or *)
LinearRecurrence[{3, -3, 1}, {1, 6, 18}, 60] (* Paolo Xausa, Nov 02 2025 *)

Crossrefs

Cf. A140065. Equals A186029(n) + 1.

Sequence in context: A180438 A202366 A185223 * A299272 A101853 A393346

Adjacent sequences: A389612 A389613 A389614 * A389616 A389617 A389618

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 02 2025

Status

approved