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%I #28 Sep 08 2022 08:45:24
%S 1,4,12,25,43,66,94,127,165,208,256,309,367,430,498,571,649,732,820,
%T 913,1011,1114,1222,1335,1453,1576,1704,1837,1975,2118,2266,2419,2577,
%U 2740,2908,3081,3259,3442,3630,3823,4021,4224,4432,4645,4863,5086,5314,5547
%N a(n) = (5*n^2 + n + 2)/2.
%C Binomial transform of (1,3,5,0,0,0...).
%H G. C. Greubel, <a href="/A116668/b116668.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F Product of Pascal's triangle as an infinite lower triangular matrix and the vector (1,3,5,0,0,0...)
%F O.g.f.: (1+x+3*x^2)/(1-x)^3. - _R. J. Mathar_, Apr 02 2008
%F a(n) = 5*n + a(n-1) - 2 (with a(0)=1) - _Vincenzo Librandi_, Nov 13 2010
%e a(3)=1*1+3*3+3*5+1*0=25.
%p a:=n->(5*n^2+n+2)/2: seq(a(n),n=0..50); # _Emeric Deutsch_, Feb 28 2006
%t s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 235, 5}] lst - _Zerinvary Lajos_, Jul 11 2009
%t LinearRecurrence[{3,-3,1}, {1,4,12}, 50] (* _G. C. Greubel_, Jan 29 2018 *)
%o (PARI) a(n)=(5*n^2+n+2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Magma) [(5*n^2 + n+2)/2: n in [0..50]]; // _G. C. Greubel_, Jan 29 2018
%o (GAP) List([0..1000],n->(5*n^2+n+2)/2); # _Muniru A Asiru_, Jan 30 2018
%Y Cf. A116666.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Feb 22 2006
%E More terms from _Emeric Deutsch_, Feb 28 2006
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