cp's OEIS Frontend

A144152 Triangle read by rows: A128174 * X; X = an infinite lower triangular matrix with a shifted Fibonacci sequence: (1, 1, 1, 2, 3, 5, 8, ...) in the main diagonal and the rest zeros.

%I A144152 #17 Feb 08 2022 23:38:05
%S A144152 1,0,1,1,0,1,0,1,0,2,1,0,1,0,3,0,1,0,2,0,5,1,0,1,0,3,0,8,0,1,0,2,0,5,
%T A144152 0,13,1,0,1,0,3,0,8,0,21,0,1,0,2,0,0,5,0,13,0,34,1,0,1,0,3,0,8,0,21,0,
%U A144152 55
%N A144152 Triangle read by rows: A128174 * X; X = an infinite lower triangular matrix with a shifted Fibonacci sequence: (1, 1, 1, 2, 3, 5, 8, ...) in the main diagonal and the rest zeros.
%C A144152 The original definition was: Eigentriangle, row sums = Fibonacci numbers.
%C A144152 Even n rows are composed of odd-indexed Fibonacci numbers interpolated with zeros.
%C A144152 Odd n rows are composed of even-indexed Fibonacci numbers with alternate zeros.
%C A144152 Sum of n-th row terms = rightmost term of next row, = F(n-1). Row sums = F(n).
%F A144152 A128174 = the matrix: (1; 0,1; 1,0,1; 0,1,0,1; ...). These operations are equivalent to termwise products of n terms of A128174 matrix row terms and an equal number of terms in (1, 1, 1, 2, 3, 5, 8, ...).
%e A144152 First few rows of the triangle =
%e A144152   1;
%e A144152   0,  1;
%e A144152   1,  0,  1;
%e A144152   0,  1,  0,  2;
%e A144152   1,  0,  1,  0,  3
%e A144152   0,  1,  0,  2,  0,  5;
%e A144152   1,  0,  1,  0,  3,  0,  8;
%e A144152   0,  1,  0,  2,  0,  5,  0, 13;
%e A144152   1,  0,  1,  0,  3,  0,  8,  0, 21;
%e A144152   ...
%e A144152 Row 5 = (1, 0, 1, 0, 3) = termwise products of (1, 0, 1, 0, 1) and (1, 1, 1, 2, 3).
%o A144152 (PARI) MT(n,k) = (1+(-1)^(n-k))/2;
%o A144152 MF(n,k) = n--; k--; if (n==k, if (n==0, 1, fibonacci(n)), 0);
%o A144152 tabl(nn) = {my(T=matrix(nn,nn, n, k, MT(n,k))); my(F=matrix(nn,nn, n, k, MF(n,k))); my(P=T*F); matrix(nn, nn, n, k, if (n>=k, P[n,k], 0));} \\ _Michel Marcus_, Mar 08 2021
%Y A144152 Cf. A000045, A128174.
%K A144152 nonn,tabl
%O A144152 1,10
%A A144152 _Gary W. Adamson_, Sep 12 2008
%E A144152 Moved a comment to the Name section. - _Omar E. Pol_, Mar 08 2021