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A309372 a(n) = n^2 - n^3 + n^4. 1

%I #29 Aug 26 2019 04:57:11

%S 0,1,12,63,208,525,1116,2107,3648,5913,9100,13431,19152,26533,35868,

%T 47475,61696,78897,99468,123823,152400,185661,224092,268203,318528,

%U 375625,440076,512487,593488,683733,783900,894691,1016832,1151073,1298188,1458975,1634256,1824877,2031708,2255643,2497600

%N a(n) = n^2 - n^3 + n^4.

%H Colin Barker, <a href="/A309372/b309372.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F From _Colin Barker_, Aug 11 2019: (Start)

%F G.f.: x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e a(4) = 4^2 - 4^3 + 4^4 = 16 - 64 + 256 = 208.

%o (Python)

%o for x in range(100):

%o print((x**2)-(x**3)+(x**4))

%o (PARI) concat(0, Vec(x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5 + O(x^40))) \\ _Colin Barker_, Aug 11 2019

%Y Cf. A132998.

%K nonn,easy

%O 0,3

%A _John H. Chakkour_, Aug 02 2019

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Last modified April 20 15:59 EDT 2024. Contains 371844 sequences. (Running on oeis4.)