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%I #27 Sep 08 2022 08:45:13
%S 30,354,4890,72354,1108650,17312754,273234810,4338079554,69107159370,
%T 1102999460754,17623571298330,281757423024354,4506141560307690,
%U 72080471098818354,1153127396812683450,18448597098193370754,295164582378232361610,4722516577573661689554
%N 1 + 4^n + 9^n + 16^n.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (30, -273, 820, -576).
%F For n > 0, a(n) = 5^(2*n+1)/(2*n+1)*sum(k = 0, 2*n + 1, (1/5)^k*C(2*n + 1, k)*B(k)) where B(k) is the k-th Bernoulli number.
%F G.f.: x*(16/(1 - 16*x) + 9/(1 - 9*x) + 4/(1 - 4*x) + 1/(1 - x)). - _Harvey P. Dale_, May 04 2011
%F a(1) = 30, a(2) = 354, a(3) = 4890, a(4) = 72354, a(n) = 30*a(n-1) - 273*a(n-2) + 820*a(n-3) - 576*a(n-4). - _Harvey P. Dale_, May 04 2011
%p A091775:=n->1+4^n+9^n+16^n: seq(A091775(n), n=1..20); # _Wesley Ivan Hurt_, Nov 26 2014
%t Table[1 + 4^n + 9^n + 16^n, {n, 20}] (* or *) LinearRecurrence[ {30, -273, 820, -576}, {30, 354, 4890, 72354}, 20] (* _Harvey P. Dale_, May 04 2011 *)
%o (Magma) [1+4^n+9^n+16^n : n in [1..20]]; // _Wesley Ivan Hurt_, Nov 26 2014
%Y Cf. A052539, A074515.
%K nonn,easy
%O 1,1
%A _Benoit Cloitre_, Mar 06 2004
%E Corrected and extended by _Harvey P. Dale_, May 04 2011
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