%I #20 Sep 08 2022 08:46:11

%S 1,253,5796,46620,213444,697788,1832292,4131036,8329860,15426684,

%T 26721828,43858332,68862276,104183100,152733924,217931868,303738372,

%U 414699516,555986340,733435164,953587908,1223732412,1551942756,1947119580,2419030404,2978349948

%N Third differences of eighth powers (A001016).

%H Luciano Ancora, <a href="/A255182/b255182.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F 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 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 Third differences: 1, 253, 5796, 46620, 213444, ... (this sequence)

%e Second differences: 1, 254, 6050, 52670, 266114, ... (A255178)

%e First differences: 1, 255, 6305, 58975, 325089, ... (A022524)

%e ---------------------------------------------------------------------

%e The seventh powers: 1, 253, 5796, 46620, 213444, ... (A001016)

%e ---------------------------------------------------------------------

%t Join[{1, 253}, Table[84 (2 n - 1) (2 n^4 - 4 n^3 + 8 n^2 - 6 n + 3), {n, 2, 30}]]

%o (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 Cf. A000542, A001016, A022524, A254642, A255178, A255181.

%K nonn,easy

%O 0,2

%A _Luciano Ancora_, Mar 18 2015

%E Edited by _Bruno Berselli_, Mar 19 2015