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A027965 T(n, 2*n-3), T given by A027960. 4

%I #13 Oct 18 2022 15:01:41

%S 3,7,15,28,47,73,107,150,203,267,343,432,535,653,787,938,1107,1295,

%T 1503,1732,1983,2257,2555,2878,3227,3603,4007,4440,4903,5397,5923,

%U 6482,7075,7703,8367,9068,9807,10585,11403,12262,13163,14107,15095,16128,17207,18333,19507,20730,22003

%N T(n, 2*n-3), T given by A027960.

%H G. C. Greubel, <a href="/A027965/b027965.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n+2) = A074742(n-1) = A008778(n) + 2 = A000297(n-1) + 3.

%F From _Ralf Stephan_, Feb 07 2004: (Start)

%F G.f.: x^2*(3 - 2*x)*(1 - x + x^2)/(1-x)^4.

%F Differences of A027966. (End)

%F From _G. C. Greubel_, Jun 30 2019: (Start)

%F a(n) = (18 - 10*n + 3*n^2 + n^3)/6.

%F E.g.f.: (-18 - 12*x + (18 - 6*x + 6*x^2 + x^3)*exp(x))/6. (End)

%t LinearRecurrence[{4,-6,4,-1}, {3,7,15,28}, 50] (* _G. C. Greubel_, Jun 30 2019 *)

%o (PARI) vector(50, n, n++; (18-10*n+3*n^2+n^3)/6) \\ _G. C. Greubel_, Jun 30 2019

%o (Magma) [(18-10*n+3*n^2+n^3)/6: n in [2..50]]; // _G. C. Greubel_, Jun 30 2019

%o (Sage) [(18-10*n+3*n^2+n^3)/6 for n in (2..50)] # _G. C. Greubel_, Jun 30 2019

%o (GAP) List([2..50], n-> (18-10*n+3*n^2+n^3)/6) # _G. C. Greubel_, Jun 30 2019

%Y A column of triangle A027011.

%K nonn,easy

%O 2,1

%A _Clark Kimberling_

%E Terms a(32) onward added by _G. C. Greubel_, Jun 30 2019

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)