A322465 Numbers on the 0-9-10-line in a spiral on an equilateral triangular lattice.

0, 9, 10, 31, 32, 65, 66, 111, 112, 169, 170, 239, 240, 321, 322, 415, 416, 521, 522, 639, 640, 769, 770, 911, 912, 1065, 1066, 1231, 1232, 1409, 1410, 1599, 1600, 1801, 1802, 2015, 2016, 2241, 2242, 2479, 2480, 2729, 2730, 2991, 2992, 3265, 3266, 3551, 3552

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 9, 10, ... in the triangle spiral.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Hans G. Oberlack, Triangle spiral line 0-9-10

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

For even n: a(n) = n*((3/2)*n+2).

For odd n: a(n) = a(n+1)-1 = (n+1)*((3/2)*(n+1)+2)-1.

From Colin Barker, Dec 18 2018: (Start)

G.f.: x*(9 + x + 3*x^2 - x^3) / ((1 - x)^3*(1 + x)^2).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.

(End)

Maple

a:= n-> `if`(n::even, n*((3/2)*n+2), (n+1)*((3/2)*(n+1)+2)-1): seq(a(n), n=0..50); # Muniru A Asiru, Dec 20 2018

Prog

(PARI) concat(0, Vec(x*(9 + x + 3*x^2 - x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ Colin Barker, Dec 18 2018

Crossrefs

Bisection (even part) gives A202804.

Sequence in context: A045483 A007252 A322653 * A353600 A119209 A329636

Adjacent sequences: A322462 A322463 A322464 * A322466 A322467 A322468

Keyword

nonn,easy

Author

Hans G. Oberlack, Dec 09 2018

Status

approved