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%I #29 Sep 08 2022 08:45:45
%S 98,354,978,2258,4578,8418,14354,23058,35298,51938,73938,102354,
%T 138338,183138,238098,304658,384354,478818,589778,719058,868578,
%U 1040354,1236498,1459218,1710818,1993698,2310354,2663378,3055458,3489378,3968018,4494354
%N a(n) = 4*n^4 + 24*n^3 + 84*n^2 + 144*n + 98.
%C Sums of 4 consecutive fourth powers.
%C Subsequence of A217844. - _Michel Marcus_, Jun 30 2013
%H Vincenzo Librandi, <a href="/A160828/b160828.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = Sum_{i=0..3} A000583(n+i) = Sum_{j=n..n+3} j^4 = A160827(n) + (n+3)^4.
%F G.f.: (18*x^4 - 72*x^3 + 188*x^2 - 136*x + 98)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009
%F a(0)=98, a(1)=354, a(2)=978, a(3)=2258, a(4)=4578, a(n)=5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Harvey P. Dale_, Mar 25 2012
%F E.g.f.: 2*(49 + 128*x + 92*x^2 + 24*x^3 + 2*x^4)*exp(x). - _G. C. Greubel_, Apr 30 2018
%p A000583 := proc(n) n^4 ; end: A160828 := proc(n) add(A000583(i),i=n..n+3) ; end: seq(A160828(n),n=0..40) ; # _R. J. Mathar_, May 29 2009
%t Table[4n^4+24n^3+84n^2+144n+98,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{98,354,978,2258,4578},40] (* _Harvey P. Dale_, Mar 25 2012 *)
%t CoefficientList[Series[(18*x^4 -72*x^3 +188*x^2 -136*x +98)/(1-x)^5, {x, 0, 50}], x] (* _G. C. Greubel_, Apr 30 2018 *)
%o (Magma) [4*n^4+24*n^3+84*n^2+144*n+98: n in [0..40]]; // _Vincenzo Librandi_, Aug 27 2011
%o (Python)
%o A160828_list, m = [], [96, 0, 80, 80, 98]
%o for _ in range(10**2):
%o A160828_list.append(m[-1])
%o for i in range(4):
%o m[i+1] += m[i] # _Chai Wah Wu_, Jan 23 2016
%o (PARI) x='x+O('x^50); Vec((18*x^4 -72*x^3 +188*x^2 -136*x +98)/(1-x)^5) \\ _G. C. Greubel_, Apr 30 2018
%K nonn,easy
%O 0,1
%A Al Hakanson (hawkuu(AT)gmail.com), May 27 2009
%E Edited and corrected by _R. J. Mathar_, May 29 2009
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