# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a144152 Showing 1-1 of 1 %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE