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%I #18 Jun 13 2015 00:55:23
%S 20,35,77,203,605,1955,6677,23723,86765,324275,1231877,4738043,
%T 18396125,71940995,282882677,1116985163,4424500685,17568076115,
%U 69883311077,278367837083,1109978272445,4429440153635,17686354389077,70651224045803,282322365983405,1128441973997555,4511225627508677,18037276107243323,72126226025905565
%N a(n) = 4^n + 6*2^n + 3^(n+1) + 10.
%C This is the sequence of fourth terms of "third partial sums of m-th powers".
%H Colin Barker, <a href="/A254363/b254363.txt">Table of n, a(n) for n = 0..1000</a>
%H Luciano Ancora, <a href="https://oeis.org/A254364/a254364.pdf">Demonstration of formulas</a>, page 2.
%H Luciano Ancora, <a href="/A254363/a254363_1.pdf">Recurrence relations for partial sums of m-th powers</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F G.f.: -(342*x^3-427*x^2+165*x-20) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - _Colin Barker_, Jan 30 2015
%F a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - _Colin Barker_, Jan 30 2015
%t Table[4^n + 6*2^n + 3^(n + 1) + 10, {n, 0, 28}] (* _Michael De Vlieger_, Jan 30 2015 *)
%o (PARI) vector(30, n, n--; 4^n + 6*2^n + 3^(n+1) + 10) \\ _Colin Barker_, Jan 30 2015
%Y Cf. A062709, A254362, A254364.
%K nonn,easy
%O 0,1
%A _Luciano Ancora_, Jan 29 2015
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