A016960 - OEIS

%I #24 Mar 31 2022 10:52:57

%S 256,10000,65536,234256,614656,1336336,2560000,4477456,7311616,

%T 11316496,16777216,24010000,33362176,45212176,59969536,78074896,

%U 100000000,126247696,157351936,193877776,236421376,285610000,342102016,406586896,479785216,562448656,655360000

%N a(n) = (6*n + 4)^4.

%H Vincenzo Librandi, <a href="/A016960/b016960.txt">Table of n, a(n) for n = 0..3000</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) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Harvey P. Dale_, Sep 23 2013

%F G.f.: 16*(16+545*x+1131*x^2+251*x^3+x^4)/(1-x)^5. - _Harvey P. Dale_, Aug 21 2021

%F From _Amiram Eldar_, Mar 31 2022: (Start)

%F a(n) = A016957(n)^4 = A016958(n)^2.

%F a(n) = 16*A016792(n).

%F Sum_{n>=0} 1/a(n) = PolyGamma(3, 2/3)/7776. (End)

%t (6*Range[0,20]+4)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1},{256,10000,65536,234256,614656},30] (* _Harvey P. Dale_, Sep 23 2013 *)

%o (Magma) [(6*n+4)^4: n in [0..40]]; // _Vincenzo Librandi_, May 06 2011

%Y Cf. A016792, A016957, A016958, A016959.

%Y Subsequence of A000583.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_