A303029 From a riddle, see Puzzling.SE link.

3, 1, 4, 8, 8, 21, 21, 62, 128, 190, 430, 831, 1451, 3030, 6143, 12286, 24361, 48850, 85497, 134347, 268694, 583208, 1071746, 2192342, 3264088, 7514425, 14042601, 24821114, 46378140, 99867664, 171066918, 270934582, 634625444, 1272514976, 2449009584, 0, 2449009584

Offset

0,1

Links

Rémy Sigrist, Table of n, a(n) for n = 0..400

Puzzling.SE, What number comes next?

Formula

a(n) = 0 for all n > 362. - Alois P. Heinz, Aug 18 2018

From Jianing Song, Dec 25 2022: (Start)

Let d_k = A000796(k+1) be the k-th digit of Pi, then a(n) = a(n-1) + a(n-2) + ... + a(n-d_{n-3}) for n >= 3.

If there exists consecutive 9 digits ...d_{k}d_{k+1}...d_{k+8}... of Pi such that d_{k+i} <= i for i = 0..8, then a(n) = 0 for all n >= k+3. The 360th to 368th digits of Pi are ...001133053..., so a(n) = 0 for all n >= 363. (End)

Example

a(0,1,2) = 3,1,4
To continue, we use the decimal expansion of Pi = 3.14159...:
a(3) = 3+1+4 (3-bonacci) = 8
a(4) = 8 (1-bonacci) = 8
a(5) = 1+4+8+8 (4-bonacci) = 21
a(6) = 21 (1-bonacci) = 21
a(7) = 21+21+8+8+4 (5-bonacci) = 62
...

Crossrefs

Cf. A000796.

Sequence in context: A329130 A057049 A245672 * A050059 A025121 A025097

Adjacent sequences: A303026 A303027 A303028 * A303030 A303031 A303032

Keyword

nonn,base,easy,less

Author

David F. Marrs, Aug 16 2018

Status

approved