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A255182 Third differences of eighth powers (A001016).

%I A255182 #20 Sep 08 2022 08:46:11
%S A255182 1,253,5796,46620,213444,697788,1832292,4131036,8329860,15426684,
%T A255182 26721828,43858332,68862276,104183100,152733924,217931868,303738372,
%U A255182 414699516,555986340,733435164,953587908,1223732412,1551942756,1947119580,2419030404,2978349948
%N A255182 Third differences of eighth powers (A001016).
%H A255182 Luciano Ancora, <a href="/A255182/b255182.txt">Table of n, a(n) for n = 0..1000</a>
%H A255182 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A255182 G.f.: (1 + 247*x + 4293*x^2 + 15619*x^3 + 15619*x^4 + 4293*x^5 + 247*x^6 + x^7)/(1 - x)^6.
%F A255182 a(n) = 84*(2*n - 1)*(2*n^4 - 4*n^3 + 8*n^2 - 6*n + 3) for n>1, a(0)=1, a(1)=253.
%e A255182 Third differences:   1, 253, 5796, 46620, 213444, ...  (this sequence)
%e A255182 Second differences:  1, 254, 6050, 52670, 266114, ...  (A255178)
%e A255182 First differences:   1, 255, 6305, 58975, 325089, ...  (A022524)
%e A255182 ---------------------------------------------------------------------
%e A255182 The seventh powers:  1, 253, 5796, 46620, 213444, ...  (A001016)
%e A255182 ---------------------------------------------------------------------
%t A255182 Join[{1, 253}, Table[84 (2 n - 1) (2 n^4 - 4 n^3 + 8 n^2 - 6 n + 3), {n, 2, 30}]]
%o A255182 (Magma) [1,253] cat [84*(2*n-1)*(2*n^4-4*n^3+8*n^2-6*n+3): n in [2..30]]; // _Vincenzo Librandi_, Mar 18 2015
%Y A255182 Cf. A000542, A001016, A022524, A254642, A255178, A255181.
%K A255182 nonn,easy
%O A255182 0,2
%A A255182 _Luciano Ancora_, Mar 18 2015
%E A255182 Edited by _Bruno Berselli_, Mar 19 2015