|
%I #16 Sep 08 2022 08:45:07
%S 1,2,6,14,32,70,150,316,658,1358,2784,5678,11534,23356,47178,95110,
%T 191440,384854,772902,1550972,3110306,6234142,12490176,25015774,
%U 50088862,100270460,200690970,401624726,803642288,1607920198,3216868854,6435401788,12873496114,25751348846
%N Row sums of triangle in A074829.
%C An elephant sequence, see A175654. For the corner squares 16 A[5] vectors, with decimal values between 43 and 424, lead to this sequence. For the central square these vectors lead to the companion sequence A175657. - _Johannes W. Meijer_, Aug 15 2010
%H G. C. Greubel, <a href="/A074878/b074878.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2).
%F From _Philippe Deléham_, Sep 20 2006: (Start)
%F a(1)=1, a(2)=2, a(3)=6, a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n>3.
%F a(n) = 3*2^(n-1) - 2*F(n+1), F(n)=A000045(n).
%F G.f.: x*(1-x+x^2)/(1-3*x+x^2+2*x^3). (End)
%F a(1)=1, a(n) = 2*(a(n-1) + F(n-2)) where the Fibonacci number F(n-2) = A000045(n-2). - Anton Vrba (antonvrba(AT)yahoo.com), Feb 06 2007
%F a(n) = 3*2^n - 2*F(n+2), with offset 0 and F(n)=A000045(n). - _Johannes W. Meijer_, Aug 15 2010
%t Table[3*2^(n-1) - 2*Fibonacci[n+1], {n, 1, 40}] (* _G. C. Greubel_, Jul 12 2019 *)
%o (PARI) vector(40, n, 3*2^(n-1) -2*fibonacci(n+1)) \\ _G. C. Greubel_, Jul 12 2019
%o (Magma) [3*2^(n-1) - 2*Fibonacci(n+1): n in [1..40]]; // _G. C. Greubel_, Jul 12 2019
%o (Sage) [3*2^(n-1) - 2*fibonacci(n+1) for n in (1..40)] # _G. C. Greubel_, Jul 12 2019
%o (GAP) List([1..40], n-> 3*2^(n-1) - 2*Fibonacci(n+1)); # _G. C. Greubel_, Jul 12 2019
%Y Cf. A000045.
%K easy,nonn
%O 1,2
%A _Joseph L. Pe_, Sep 30 2002
%E More terms from _Philippe Deléham_, Sep 20 2006
%E Terms a(23) onward added by _G. C. Greubel_, Jul 12 2019
|
