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

1,2

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

Links

Table of n, a(n) for n=1..66.

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

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)

Example

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;

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.

Sequence in context: A377094 A108228 A127008 * A064274 A035513 A343646

Adjacent sequences: A199532 A199533 A199534 * A199536 A199537 A199538

Keyword

nonn,tabl

Author

Casey Mongoven, Nov 07 2011

Extensions

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

Status

approved