login
First column in maze arrangement of natural numbers A081344.
3

%I #15 Sep 08 2022 08:45:09

%S 1,2,9,10,25,26,49,50,81,82,121,122,169,170,225,226,289,290,361,362,

%T 441,442,529,530,625,626,729,730,841,842,961,962,1089,1090,1225,1226,

%U 1369,1370,1521,1522,1681,1682,1849,1850,2025,2026,2209,2210,2401,2402,2601

%N First column in maze arrangement of natural numbers A081344.

%C Interleaves odd squares A016754 with central polygonal numbers A001844.

%H Vincenzo Librandi, <a href="/A081346/b081346.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F a(n) = n^2 + n + 1 + n*(-1)^n.

%F a(2*n) = A016754(n), a(2*n+1) = 2*A001844(n).

%F G.f.: (1 + x + 5*x^2 - x^3 + 2*x^4)/((1-x)^3*(1+x)^2). [_Colin Barker_, Sep 03 2012]

%o (Magma) [n^2+n+1+n*(-1)^n: n in [0..50]]; // _Vincenzo Librandi_, Sep 05 2011

%Y Cf. A081345.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 19 2003