A199535 Clark Kimberling's even first column Stolarsky array read by antidiagonals.

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, 23, 16, 34, 76, 63, 71, 50, 37, 25, 20, 55, 123, 102, 115, 81, 60, 41, 33, 22, 89, 199, 165, 186, 131, 97, 66, 53, 35, 26, 144, 322, 267, 301, 212, 157, 107, 86, 57, 43, 28

Offset: 1

Author

Casey Mongoven, Nov 07 2011

Keywords

• nonn
• tabl

Comments

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

Examples

			The even first column stolarsky array (EFC array), northwest corner:
  1......2.....3.....5.....8....13....21....34....55....89...144 ... A000045;
  4......7....11....18....29....47....76...123...199...322...521 ... A000032;
  6......9....15....24....39....63...102...165...267...432...699 ... A022086;
  10....17....27....44....71...115...186...301...487...788..1275 ... A022120;
  12....19....31....50....81...131...212...343...555...898..1453 ... A013655;
  14....23....37....60....97...157...254...411...665..1076..1741 ... A000285;
  16....25....41....66...107...173...280...453...733..1186..1919 ... A022113;
  20....33....53....86...139...225...364...589...953..1542..2495 ... A022096;
  22....35....57....92...149...241...390...631..1021..1652..2673 ... A022130;
Antidiagonal rows (T(n, k)):
   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, 23, 16;
  34,  76,  63,  71, 50, 37, 25, 20;
  55, 123, 102, 115, 81, 60, 41, 33, 22;
		

Links

• Clark Kimberling, The first column of an interspersion, Fibonacci Quarterly 32 (1994), pp. 301-314.

Crossrefs

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

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

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

Formula

From G. C. Greubel, Jun 23 2022: (Start)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Extensions

More terms added by G. C. Greubel, Jun 23 2022