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A081272 Downward vertical of triangular spiral in A051682. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

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

Sequence in context: A157530 A253053 A166080 * A318293 A027026 A251195

Adjacent sequences:  A081269 A081270 A081271 * A081273 A081274 A081275

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 15 2003

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)