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A053298 Partial sums of A027964. 4

%I

%S 1,8,34,107,281,654,1397,2801,5353,9859,17643,30869,53062,89951,

%T 150833,250780,414210,680665,1114160,1818310,2960806,4813018,7814074,

%U 12674542,20544191,33283434,53902532,87272241,141273663,228658744

%N Partial sums of A027964.

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

%H G. C. Greubel, <a href="/A053298/b053298.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,15,-5,-4,4,-1)

%F a(n) = 3*F(n+10) + F(n+9) - (3*n^4 + 58*n^3 + 489*n^2 + 2234*n + 4752)/24, where F(.) are the Fibonacci numbers (A000045).

%F a(n) = a(n-1) + a(n-2) + (3*n+4)*C(n+3, 3)/4.

%F G.f.: (1 + 2*x)/((1 - x - x^2)*(1 - x)^5). - _R. J. Mathar_, Nov 28 2008

%t LinearRecurrence[{6,-14,15,-5,-4,4,-1},{1,8,34,107,281,654,1397},30] (* _Harvey P. Dale_, May 09 2018 *)

%t CoefficientList[Series[(1+2x)/((1-x-x^2)(1-x)^5), {x,0,50}], x] (* _G. C. Greubel_, May 24 2018 *)

%o (PARI) x='x+O('x^30); Vec((1+2*x)/((1-x-x^2)*(1-x)^5)) \\ _G. C. Greubel_, May 24 2018

%o (MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x)/((1-x-x^2)*(1-x)^5))); // _G. C. Greubel_, May 24 2018

%Y Cf. A027964 and A000204.

%Y A column in triangular array A027960.

%Y Cf. A137176 (row k=5).

%K nonn,easy

%O 0,2

%A _Barry E. Williams_, Mar 04 2000

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Last modified February 20 06:26 EST 2019. Contains 320332 sequences. (Running on oeis4.)