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%I #19 Dec 25 2022 03:52:28
%S 1,225,841,1849,3249,5041,7225,9801,12769,16129,19881,24025,28561,
%T 33489,38809,44521,50625,57121,64009,71289,78961,87025,95481,104329,
%U 113569,123201,133225,143641,154449,165649,177241,189225,201601,214369,227529,241081
%N a(n) = (14*n+1)^2.
%C Number of rats in population after n years, starting with one rat at year 0 (see A016754 for more details).
%H Vincenzo Librandi, <a href="/A134934/b134934.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F O.g.f.: (1+222*x+169*x^2)/(1-x)^3 = 169/(1-x) - 560/(1-x)^2 + 392/(1-x)^3. - _R. J. Mathar_, Jan 31 2008
%F a(n) = A016754(7*n).
%F E.g.f.: (1 + 224*x + 196*x^2)*exp(x). - _G. C. Greubel_, Dec 24 2022
%t (14*Range[0,50]+1)^2 (* _G. C. Greubel_, Dec 24 2022 *)
%o (Magma) [(14*n+1)^2: n in [0..50]]; // _Vincenzo Librandi_, Sep 06 2011
%o (PARI) a(n)=(14*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (SageMath) [(14*n+1)^2 for n in range(51)] # _G. C. Greubel_, Dec 24 2022
%Y Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m=3), A016814 (m=4), A016862 (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), this sequence (m=14).
%Y Cf. A016754.
%K nonn,easy
%O 0,2
%A _Hans Isdahl_, Jan 26 2008
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