A081272 Downward vertical of triangular spiral in A051682.

1, 25, 85, 181, 313, 481, 685, 925, 1201, 1513, 1861, 2245, 2665, 3121, 3613, 4141, 4705, 5305, 5941, 6613, 7321, 8065, 8845, 9661, 10513, 11401, 12325, 13285, 14281, 15313, 16381, 17485, 18625, 19801, 21013, 22261, 23545, 24865, 26221, 27613, 29041, 30505

Offset

0,2

Comments

Reflection of A081271 in the horizontal A051682.

Binomial transform of (1, 24, 36, 0, 0, 0, .....).

One of the six verticals of a triangular spiral which starts with 1 (see the link). Other verticals are A060544, A081589, A080855, A157889, A038764. - Yuriy Sibirmovsky, Sep 18 2016.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Kaie Kubjas, Luca Sodomaco, and Elias Tsigaridas, Exact solutions in low-rank approximation with zeros, arXiv:2010.15636 [math.AG], 2020.

Yuriy Sibirmovsky, Six verticals of the triangular spiral.

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

Formula

a(n) = C(n, 0) + 24*C(n, 1) + 36*C(n, 2).

a(n) = 18*n^2 + 6*n + 1.

G.f.: (1 + 22*x + 13*x^2)/(1 - x)^3.

E.g.f.: exp(x)*(1 + 24*x + 18*x^2). - Stefano Spezia, Mar 07 2023

Mathematica

Table[n^2 + (n + 1)^2, {n, 0, 300, 3}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 25, 85}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
Table[n^2 + (n + 1)^2, {n, 0, 150, 3}] (* Vincenzo Librandi, Aug 07 2013 *)

Prog

(PARI) x='x+O('x^99); Vec((1+22*x+13*x^2)/(1-x)^3) \\ Altug Alkan, Sep 18 2016

Crossrefs

Cf. A051682.

Cf. A062741, A060544, A081589, A080855, A157889, A038764.

Sequence in context: A365249 A166080 A371016 * A318293 A027026 A251195

Adjacent sequences: A081269 A081270 A081271 * A081273 A081274 A081275

Keyword

nonn,easy

Author

Paul Barry, Mar 15 2003

Status

approved