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%I #15 Jan 16 2018 02:39:59
%S 1,12,32,61,99,146,202,267,341,424,516,617,727,846,974,1111,1257,1412,
%T 1576,1749,1931,2122,2322,2531,2749,2976,3212,3457,3711,3974,4246,
%U 4527,4817,5116,5424,5741,6067,6402,6746,7099,7461,7832,8212,8601,8999,9406
%N Diagonal of triangular spiral in A051682.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = C(n, 0) + 11C(n, 1) + 9C(n, 2); binomial transform of (1, 11, 9, 0, 0, 0, ...).
%F a(n) = (9n^2 + 13n+2)/2.
%F G.f.: (1 + 9x - x^2)/(1-x)^3.
%F a(n) = 9*n + a(n-1) + 2 (with a(0)=1). - _Vincenzo Librandi_, Aug 08 2010
%e a(1) = 9*1 + 1 + 2 = 12;
%e a(2) = 9*2 + 12 + 2 = 32;
%e a(3) = 9*3 + 32 + 2 = 61.
%o (PARI) a(n)=(9*n^2+13*n+2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A081267.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 15 2003
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