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%I #42 Sep 08 2022 08:45:59
%S 2,4,12,18,31,41,59,73,96,114,142,164,197,223,261,291,334,368,416,454,
%T 507,549,607,653,716,766,834,888,961,1019,1097,1159,1242,1308,1396,
%U 1466,1559,1633,1731,1809,1912,1994,2102,2188,2301,2391,2509,2603,2726,2824,2952
%N a(n) = (6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16 + 1.
%C For an origin of this sequence, see the triangular spiral illustrated in the Links section.
%C First bisection gives A117625 (without the initial term).
%H Bruno Berselli, <a href="/A198392/b198392.txt">Table of n, a(n) for n = 0..1000</a>
%H Bruno Berselli, <a href="http://www.base5forum.it/upload/A_198392.jpg">Illustration of initial terms</a>.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F G.f.: (2+2*x+4*x^2+2*x^3-x^4)/((1+x)^2*(1-x)^3).
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
%F a(n)-a(-n-1) = A168329(n+1).
%F a(n)+a(n-1) = A102214(n).
%F a(2n)-a(2n-1) = A016885(n).
%F a(2n+1)-a(2n) = A016825(n).
%t LinearRecurrence[{1,2,-2,-1,1},{2,4,12,18,31},60] (* _Harvey P. Dale_, Jun 15 2022 *)
%o (PARI) for(n=0, 50, print1((6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16+1", "));
%o (Magma) [(6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16+1: n in [0..50]];
%Y Cf. A152832 (by Superseeker).
%Y Cf. sequences related to the triangular spiral: A022266, A022267, A027468, A038764, A045946, A051682, A062708, A062725, A062728, A062741, A064225, A064226, A081266-A081268, A081270-A081272, A081275 [incomplete list].
%K nonn,easy
%O 0,1
%A _Bruno Berselli_, Oct 25 2011
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