A199535 - OEIS

%I #26 Jun 23 2022 13:47:48

%S 1,2,4,3,7,6,5,11,9,10,8,18,15,17,12,13,29,24,27,19,14,21,47,39,44,31,

%T 23,16,34,76,63,71,50,37,25,20,55,123,102,115,81,60,41,33,22,89,199,

%U 165,186,131,97,66,53,35,26,144,322,267,301,212,157,107,86,57,43,28

%N Clark Kimberling's even first column Stolarsky array read by antidiagonals.

%C The rows of the array can be seen to have the form A(n, k) = p(n)*Fibonacci(k) + q(n)*Fibonacci(k+1) where p(n) is the sequence {0, 1, 3, 3, 3, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, ...}_{n >= 1} and q(n) is the sequence {1, 3, 3, 7, 2, 9, 9, 13, 13, 17, 17, 19, 19, 23, 23, 25, ...}_{n >= 1}. - _G. C. Greubel_, Jun 23 2022

%H Clark Kimberling, <a href="http://www.fq.math.ca/Scanned/32-4/kimberling.pdf">The first column of an interspersion</a>, Fibonacci Quarterly 32 (1994), pp. 301-314.

%F From _G. C. Greubel_, Jun 23 2022: (Start)

%F T(n, 1) = A000045(n+1).

%F T(n, 2) = A000032(n+1), n >= 2.

%F T(n, 3) = A022086(n) = A097135(n), n >= 3.

%F T(n, 4) = A022120(n-2), n >= 4.

%F T(n, 5) = A013655(n-1), n >= 5.

%F T(n, 6) = A000285(n-2), n >= 6.

%F T(n, 7) = A022113(n-4), n >= 7.

%F T(n, 8) = A022096(n-4), n >= 8.

%F T(n, 9) = A022130(n-6), n >= 9.

%F T(n, 10) = A022098(n-5), n >= 10.

%F T(n, 11) = A022095(n-7), n >= 11.

%F T(n, 12) = A022121(n-8), n >= 12.

%F T(n, 13) = A022388(n-10), n >= 13.

%F T(n, 14) = A022122(n-10), n >= 14.

%F T(n, 15) = A022097(n-10), n >= 15.

%F T(n, 16) = A022088(n-10), n >= 16.

%F T(n, 17) = A022390(n-14), n >= 17.

%F T(n, n) = A199536(n).

%F T(n, n-1) = A199537(n-1), n >= 2. (End)

%e The even first column stolarsky array (EFC array), northwest corner:

%e   1......2.....3.....5.....8....13....21....34....55....89...144 ... A000045;

%e   4......7....11....18....29....47....76...123...199...322...521 ... A000032;

%e   6......9....15....24....39....63...102...165...267...432...699 ... A022086;

%e   10....17....27....44....71...115...186...301...487...788..1275 ... A022120;

%e   12....19....31....50....81...131...212...343...555...898..1453 ... A013655;

%e   14....23....37....60....97...157...254...411...665..1076..1741 ... A000285;

%e   16....25....41....66...107...173...280...453...733..1186..1919 ... A022113;

%e   20....33....53....86...139...225...364...589...953..1542..2495 ... A022096;

%e   22....35....57....92...149...241...390...631..1021..1652..2673 ... A022130;

%e Antidiagonal rows (T(n, k)):

%e    1;

%e    2,   4;

%e    3,   7,   6;

%e    5,  11,   9,  10;

%e    8,  18,  15,  17, 12;

%e   13,  29,  24,  27, 19, 14;

%e   21,  47,  39,  44, 31, 23, 16;

%e   34,  76,  63,  71, 50, 37, 25, 20;

%e   55, 123, 102, 115, 81, 60, 41, 33, 22;

%Y Cf. A000032, A000045, A000285, A013655, A022086, A022088, A022095.

%Y Cf. A022096, A022097, A022113, A022120, A022121, A022122, A022130.

%Y Cf. A022388, A022390, A035506, A035513, A097135, A199536, A199537.

%K nonn,tabl

%O 1,2

%A _Casey Mongoven_, Nov 07 2011

%E More terms added by _G. C. Greubel_, Jun 23 2022