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A131411 Triangle read by rows: T(n,k) = Fibonacci(n) + Fibonacci(k) - 1.

%I A131411 #21 Sep 08 2022 08:45:31
%S A131411 1,1,1,2,2,3,3,3,4,5,5,5,6,7,9,8,8,9,10,12,15,13,13,14,15,17,20,25,21,
%T A131411 21,22,23,25,28,33,41,34,34,35,36,38,41,46,54,67,55,55,56,57,59,62,67,
%U A131411 75,88,109,89,89,90,91,93,96,101,109,122,143,177,144,144,145,146,148,151,156,164,177,198,232,287
%N A131411 Triangle read by rows: T(n,k) = Fibonacci(n) + Fibonacci(k) - 1.
%C A131411 Left column = Fibonacci numbers. Right column = A001595: (1, 1, 3, 5, 9, 15, 25,...).
%C A131411 Row sums = A131412: (1, 2, 7, 15, 32, 62, 117, 214,...).
%H A131411 Andrew Howroyd, <a href="/A131411/b131411.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)
%F A131411 Equals A131410 + A104763 - A000012 as infinite lower triangular matrices.
%e A131411 First few rows of the triangle are:
%e A131411    1;
%e A131411    1,  1;
%e A131411    2,  2,  3;
%e A131411    3,  3,  4,  5;
%e A131411    5,  5,  6,  7,  9;
%e A131411    8,  8,  9, 10, 12, 15;
%e A131411   13, 13, 14, 15, 17, 20, 25;
%e A131411   21, 21, 22, 23, 25, 28, 33, 41;
%e A131411   ...
%t A131411 With[{F=Fibonacci}, Table[F[n]+F[k]-1, {n,15}, {k,n}]//Flatten] (* _G. C. Greubel_, Jul 13 2019 *)
%o A131411 (PARI) T(n,k) = if(k<=n, fibonacci(n) + fibonacci(k) - 1, 0); \\ _Andrew Howroyd_, Aug 10 2018
%o A131411 (Magma) F:=Fibonacci; [F(n)+F(k)-1: k in [1..n], n in [1..15]]; // _G. C. Greubel_, Jul 13 2019
%o A131411 (Sage) f=fibonacci; [[f(n)+f(k)-1 for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Jul 13 2019
%o A131411 (GAP) F:=Fibonacci;; Flat(List([1..15], n-> List([1..n], k-> F(n) +F(k) -1 ))); # _G. C. Greubel_, Jul 13 2019
%Y A131411 Row sums are A131412.
%Y A131411 Cf. A000012, A000045, A001595, A104763, A127647, A131410.
%K A131411 nonn,tabl
%O A131411 1,4
%A A131411 _Gary W. Adamson_, Jul 08 2007
%E A131411 Name changed and terms a(56) and beyond from _Andrew Howroyd_, Aug 10 2018