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From a riddle, see Puzzling.SE link.
1

%I #39 Dec 25 2022 08:30:44

%S 3,1,4,8,8,21,21,62,128,190,430,831,1451,3030,6143,12286,24361,48850,

%T 85497,134347,268694,583208,1071746,2192342,3264088,7514425,14042601,

%U 24821114,46378140,99867664,171066918,270934582,634625444,1272514976,2449009584,0,2449009584

%N From a riddle, see Puzzling.SE link.

%H Rémy Sigrist, <a href="/A303029/b303029.txt">Table of n, a(n) for n = 0..400</a>

%H Puzzling.SE, <a href="https://puzzling.stackexchange.com/questions/69357/what-number-comes-next/69391">What number comes next?</a>

%F a(n) = 0 for all n > 362. - _Alois P. Heinz_, Aug 18 2018

%F From _Jianing Song_, Dec 25 2022: (Start)

%F 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.

%F 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)

%e a(0,1,2) = 3,1,4

%e To continue, we use the decimal expansion of Pi = 3.14159...:

%e a(3) = 3+1+4 (3-bonacci) = 8

%e a(4) = 8 (1-bonacci) = 8

%e a(5) = 1+4+8+8 (4-bonacci) = 21

%e a(6) = 21 (1-bonacci) = 21

%e a(7) = 21+21+8+8+4 (5-bonacci) = 62

%e ...

%Y Cf. A000796.

%K nonn,base,easy,less

%O 0,1

%A _David F. Marrs_, Aug 16 2018