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A273624 a(n) = (1/11)*(Fibonacci(4*n) + Fibonacci(6*n)).

%I A273624 #19 Sep 08 2022 08:46:16
%S A273624 1,15,248,4305,76255,1361520,24384737,437245935,7843863784,
%T A273624 140737371825,2525326494911,45314438127840,813129752279233,
%U A273624 14590988151618255,261824431125415640,4698247224097107345,84306614992412658847,1512820749915870503760,27146466385039244529569
%N A273624 a(n) = (1/11)*(Fibonacci(4*n) + Fibonacci(6*n)).
%C A273624 This is a divisibility sequence: if n divides m then a(n) divides a(m). More generally, if r is an even integer then the sequence Fibonacci(r*n) + Fibonacci((r + 2)*n) is a divisibility sequence. See A215466 for the case r = 2.
%C A273624 Also, the sequence s(n) := Fibonacci(4*n) + Fibonacci(6*n) + ... + Fibonacci((2*k + 2)*n) is a divisibility sequence when k is a positive integer that is not a multiple of 3.
%H A273624 G. C. Greubel, <a href="/A273624/b273624.txt">Table of n, a(n) for n = 1..795</a>
%H A273624 P. Bala, <a href="/A273622/a273622.pdf">Lucas sequences and divisibility sequences</a>
%H A273624 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (25,-128,25,-1).
%F A273624 a(n) = -a(-n).
%F A273624 a(n) = 25*a(n-1) - 128*a(n-2) + 25*a(n-3) - a(n-4).
%F A273624 O.g.f. (x^2 - 10*x + 1)/((x^2 - 7*x + 1)*(x^2 - 18*x + 1)).
%p A273624 #A273624
%p A273624 with(combinat):
%p A273624 seq(1/11*(fibonacci(4n) + fibonacci(6n)), n = 1..20);
%t A273624 LinearRecurrence[{25,-128,25,-1},{1, 15, 248, 4305},100] (* _G. C. Greubel_, Jun 02 2016 *)
%t A273624 Table[1/11 (Fibonacci[4 n] + Fibonacci[6 n]), {n, 1, 30}] (* _Vincenzo Librandi_, Jun 02 2016 *)
%o A273624 (Magma) [1/11*(Fibonacci(4*n)+Fibonacci(6*n)): n in [1..25]]; // _Vincenzo Librandi_, Jun 02 2016
%o A273624 (PARI) a(n)=(fibonacci(4*n) + fibonacci(6*n))/11 \\ _Charles R Greathouse IV_, Jun 08 2016
%Y A273624 Cf. A000045, A049673, A215466, A273623, A273625.
%K A273624 nonn,easy
%O A273624 1,2
%A A273624 _Peter Bala_, May 29 2016