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%I #15 Sep 08 2022 08:44:49
%S 1,6,19,47,101,199,370,661,1148,1954,3278,5442,8967,14696,23993,39065,
%T 63483,103025,167040,270655,438346,709716,1148844,1859412,3009181,
%U 4869594,7879855,12750611,20631713,33383659,54016798,87401977,141420392,228824086,370246298,599072310,969320643
%N T(n,n+3), T given by A027960.
%H G. C. Greubel, <a href="/A027963/b027963.txt">Table of n, a(n) for n = 3..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,1,2,-1).
%F G.f.: x^3*(1+2*x)/((1-x)^3*(1-x-x^2)). Differences of A027964. - _Ralf Stephan_, Feb 07 2004
%F a(n) = Lucas(n+4) - (3*n^2 + 5*n + 14)/2.
%t t[_, 0] = 1; t[_, 1] = 3; t[n_, k_] /; (k == 2*n) = 1; t[n_, k_] := t[n, k] = t[n-1, k-2] + t[n-1, k-1]; Table[t[n, n+3], {n, 3, 33}] (* _Jean-François Alcover_, Dec 27 2013 *)
%t Table[LucasL[n+4] -(3*n^2+5*n+14)/2, {n,3,40}] (* _G. C. Greubel_, Jun 01 2019 *)
%o (PARI) {a(n) = fibonacci(n+5) + fibonacci(n+3) - (3*n^2+5*n+14)/2}; \\ _G. C. Greubel_, Jun 01 2019
%o (Magma) [Lucas(n+4) -(3*n^2+5*n+14)/2: n in [3..40]]; // _G. C. Greubel_, Jun 01 2019
%o (Sage) [lucas_number2(n+4,1,-1) - (3*n^2+5*n+14)/2 for n in (3..40)] # _G. C. Greubel_, Jun 01 2019
%o (GAP) List([3..40], n-> Lucas(1,-1,n+4)[2] - (3*n^2+5*n+14)/2 ) # _G. C. Greubel_, Jun 01 2019
%Y Cf. A000032.
%K nonn
%O 3,2
%A _Clark Kimberling_
%E Terms a(34) onward added by _G. C. Greubel_, Jun 01 2019
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