A355429 Square array T(n, k), n >= 0, k > 0, read by antidiagonals, where T(0, k) = A001906(k) for k > 0 and where T(n, k) = n - A130312(n) + A000045(2k + A072649(n)) for n > 0, k > 0.

1, 2, 3, 4, 5, 8, 6, 9, 13, 21, 7, 14, 22, 34, 55, 10, 15, 35, 56, 89, 144, 11, 23, 36, 90, 145, 233, 377, 12, 24, 57, 91, 234, 378, 610, 987, 16, 25, 58, 146, 235, 611, 988, 1597, 2584, 17, 37, 59, 147, 379, 612, 1598, 2585, 4181, 6765, 18, 38, 92, 148, 380, 989

Offset

1,2

Comments

Each positive integer occurs exactly once, so this sequence is a permutation of the natural numbers.

Links

Table of n, a(n) for n=1..61.

Index entries for sequences that are permutations of the natural numbers

Formula

T(0, k) = A001906(k) for k > 0.

T(n, k) = n - A130312(n) + A000045(2k + A072649(n)) for n > 0, k > 0.

Example

Square array begins:
   1,  3,  8,  21,  55,  144,  377,   987, ...
   2,  5, 13,  34,  89,  233,  610,  1597, ...
   4,  9, 22,  56, 145,  378,  988,  2585, ...
   6, 14, 35,  90, 234,  611, 1598,  4182, ...
   7, 15, 36,  91, 235,  612, 1599,  4183, ...
  10, 23, 57, 146, 379,  989, 2586,  6767, ...
  11, 24, 58, 147, 380,  990, 2587,  6768, ...
  12, 25, 59, 148, 381,  991, 2588,  6769, ...
  16, 37, 92, 236, 613, 1600, 4184, 10949, ...

Prog

(PARI) b1(n)=local(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2) \\ A072649
T(n, k)=if(n==0, fibonacci(2*k), n - fibonacci(b1(n)) + fibonacci(2*k + b1(n)))

Crossrefs

Cf. A000045, A001906, A072649, A130312.

Sequence in context: A085176 A354125 A339024 * A192179 A118462 A219360

Adjacent sequences: A355426 A355427 A355428 * A355430 A355431 A355432

Keyword

nonn,tabl

Author

Mikhail Kurkov, Jul 20 2022 [verification needed]

Status

approved