# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a175011
Showing 1-1 of 1

%I A175011 #9 Mar 30 2024 23:08:41
%S A175011 1,1,2,1,2,5,1,2,2,16,1,2,2,5,45,1,2,2,2,12,125,1,2,2,2,5,24,341,1,2,
%T A175011 2,2,2,12,48,918,1,2,2,2,2,7,18,97,2453,1,2,2,2,2,2,16,28,195,6515
%N A175011 Triangle read by rows, antidiagonals of an array generated from INVERT transforms of variants of (1, 2, 3, ...).
%C A175011 Row sums = A001906, the even-indexed Fibonacci numbers starting (1, 3, 8, 21, ...).
%F A175011 Given S(x) = (1 + 2x + 3x^2 + ...), where (1, 2, 3, ...) = the INVERTi transform of (1, 3, 8, 21, 55, ...); k-th row of the array = INVERT transform of S(x^k). Take finite differences of array columns starting from the topmost "1"; becoming rows of the triangle.
%e A175011 First few rows of the array:
%e A175011   1, 3, 8, 21, 55, 144, 377, 987, 2584, ...
%e A175011   1, 1, 3,  5, 10,  19,  36,  69,  131, ...
%e A175011   1, 1, 1,  3,  5,   7,  12,  21,   34, ...
%e A175011   1, 1, 1,  1,  3,   5,   7,   9,   16, ...
%e A175011   1, 1, 1,  1,  1,   3,   5,   7,    9, ...
%e A175011   1, 1, 1,  1,  1,   1,   3,   5,    7, ...
%e A175011   ...
%e A175011 Taking finite differences from the bottom to top starting with the last "1" we obtain triangle A175011:
%e A175011   1;
%e A175011   1, 2;
%e A175011   1, 2, 5;
%e A175011   1, 2, 2, 16;
%e A175011   1, 2, 2,  5, 45;
%e A175011   1, 2, 2,  2, 12, 125;
%e A175011   1, 2, 2,  2,  5,  24, 341;
%e A175011   1, 2, 2,  2,  2,  12,  48, 918;
%e A175011   1, 2, 2,  2,  2,   7,  18,  97, 2453;
%e A175011   1, 2, 2,  2,  2,   2,  16,  28,  195, 6515;
%e A175011   ...
%Y A175011 Cf. A001906.
%K A175011 nonn,tabl
%O A175011 1,3
%A A175011 _Gary W. Adamson_, Apr 03 2010

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE