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

Author

David F. Marrs, Aug 16 2018

Keywords

• nonn
• base
• easy
• less

Examples

			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
...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..400
• Puzzling.SE, What number comes next?

Crossrefs

Cf. A000796.

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)