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A255178 Second differences of eighth powers (A001016).

%I A255178 #46 Aug 26 2024 17:11:03
%S A255178 1,254,6050,52670,266114,963902,2796194,6927230,15257090,30683774,
%T A255178 57405602,101263934,170126210,274309310,427043234,644975102,948713474,
%U A255178 1363412990,1919399330,2652834494,3606422402,4830154814,6382097570,8329217150,10748247554
%N A255178 Second differences of eighth powers (A001016).
%H A255178 Luciano Ancora, <a href="/A255178/b255178.txt">Table of n, a(n) for n = 0..1000</a>
%H A255178 Luciano Ancora, <a href="https://upload.wikimedia.org/wikipedia/commons/f/fe/Sum_of_powers.pdf">Sums of powers of positive integers and their recurrence relations</a>, section 0.5.
%H A255178 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A255178 G.f.: (1 + x)*(1 + 246*x + 4047*x^2 + 11572*x^3 + 4047*x^4 + 246*x^5 + x^6)/(1 - x)^7.
%F A255178 a(n) = 2*(28*n^6 + 70*n^4 + 28*n^2 + 1) for n>0, a(0)=1.
%e A255178 Second differences:  1, 254, 6050, 52670, 266114, ... (this sequence)
%e A255178 First differences:   1, 255, 6305, 58975, 325089, ... (A022524)
%e A255178 ----------------------------------------------------------------------
%e A255178 The eighth powers:   1, 256, 6561, 65536, 390625, ... (A001016)
%e A255178 ----------------------------------------------------------------------
%e A255178 First partial sums:  1, 257, 6818, 72354, 462979, ... (A000542)
%e A255178 Second partial sums: 1, 258, 7076, 79430, 542409, ... (A253636)
%e A255178 Third partial sums:  1, 259, 7335, 86765, 629174, ... (A254642)
%e A255178 Fourth partial sums: 1, 260, 7595, 94360, 723534, ... (A254647)
%t A255178 Join[{1}, Table[2 (28 n^6 + 70 n^4 + 28 n^2 + 1), {n, 1, 30}]]
%t A255178 Join[{1},Differences[Range[0,30]^8,2]] (* _Harvey P. Dale_, Aug 26 2024 *)
%o A255178 (Magma) [n eq 0 select 1 else 2*(28*n^6+70*n^4+28*n^2+1): n in [0..30]]; // _Vincenzo Librandi_, Mar 12 2015
%Y A255178 Cf. A000542, A001016, A022524, A253636, A254642, A254647, A255177.
%K A255178 nonn,easy
%O A255178 0,2
%A A255178 _Luciano Ancora_, Feb 21 2015
%E A255178 Edited by _Bruno Berselli_, Mar 19 2015