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A159742 If an array is made of columns of -nacci sequences (Fibonacci, tribonacci, etc.), all starting with 1,1,2,..., the NW-to-SE diagonals can be extended by computation. This sequence is diagonal 6. See A159741 for details.

%I A159742 #16 Sep 08 2022 08:45:44
%S A159742 13,44,108,236,492,1004,2028,4076,8172,16364,32748,65516,131052,
%T A159742 262124,524268,1048556,2097132,4194284,8388588,16777196,33554412,
%U A159742 67108844,134217708,268435436,536870892,1073741804,2147483628,4294967276,8589934572,17179869164
%N A159742 If an array is made of columns of -nacci sequences (Fibonacci, tribonacci, etc.), all starting with 1,1,2,..., the NW-to-SE diagonals can be extended by computation. This sequence is diagonal 6. See A159741 for details.
%H A159742 G. C. Greubel, <a href="/A159742/b159742.txt">Table of n, a(n) for n = 1..1000</a>
%H A159742 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A159742 From _R. J. Mathar_, Apr 22 2009: (Start)
%F A159742 a(n) = 3*a(n-1) - 2*a(n-2), n>3.
%F A159742 a(n) = 16*2^n - 20, n>1. (End)
%p A159742 T := proc(n,m) option remember ; if n < 0 then 0; elif n <= 1 then 1; elif n = 2 then 2; else add(procname(n-i,m),i=1..m) ; fi: end: A159742 := proc(n) T(n+5,n+1) ; end: seq(A159742(n),n=1..40) ; # _R. J. Mathar_, Apr 22 2009
%t A159742 CoefficientList[Series[(2*z^2 + 5*z + 13)/(2*z^2 - 3*z + 1), {z, 0, 100}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 08 2011 *)
%t A159742 Join[{13}, Table[4*(2^(n + 2) - 5), {n, 2, 50}]] (* _G. C. Greubel_, May 22 2018 *)
%t A159742 LinearRecurrence[{3,-2},{13,44,108},30] (* _Harvey P. Dale_, Jul 10 2018 *)
%o A159742 (PARI) for(n=1, 30, print1(if(n==1, 13, 4*(2^(n+2) - 5)), ", ")) \\ _G. C. Greubel_, May 22 2018
%o A159742 (Magma) [13] cat [4*(2^(n+2) - 5): n in [2..30]]; // _G. C. Greubel_, May 22 2018
%K A159742 nonn
%O A159742 1,1
%A A159742 Al Hakanson (hawkuu(AT)gmail.com), Apr 20 2009
%E A159742 More terms from _R. J. Mathar_, Apr 22 2009