A309560 a(1) = a(2) = 1, a(3) = 2, a(4) = 3, a(5) = 5, a(6) = a(7) = 6, a(8) = 7; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) + a(n-a(n-4)) for n > 8.

1, 1, 2, 3, 5, 6, 6, 7, 8, 9, 11, 11, 10, 12, 13, 16, 15, 14, 16, 17, 20, 19, 17, 20, 23, 22, 23, 23, 24, 25, 26, 27, 27, 27, 29, 30, 31, 32, 30, 33, 35, 34, 34, 37, 38, 37, 36, 42, 38, 40, 42, 41, 45, 41, 43, 47, 48, 48, 49, 43, 45, 53, 52, 58, 44, 48, 54, 58

Offset: 1

Author

Altug Alkan and Rémy Sigrist, Aug 07 2019

Keywords

• nonn
• look

Comments

This sequence is well defined for n = 1..1000000000; however, it is not known if this sequence is defined for all positive n.

Examples

			a(10) = a(10-a(9)) + a(10-a(8)) + a(10-a(7)) + a(10-a(6)) = a(10-8) + a(10-7) + a(10-6) + a(10-6) = a(2) + a(3) + a(4) + a(4) = 1 + 2 + 3 + 3 = 9.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Density plot of the first 10000000 terms
• Rémy Sigrist, C++ program to search for this type of sequences
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A005185, A292351.

Programs

Magma

I:=[1,1,2,3,5,6,6,7];[n le 8 select I[n] else Self(n-Self(n-1))+Self(n-Self(n-2))+Self(n-Self(n-3)) + Self(n-Self(n-4)): n in [1..70]]; // Marius A. Burtea, Aug 07 2019

PARI

a = vector(68); a[1] = a[2] = 1; a[3] = 2; a[4] = 3; a[5] = 5; a[6] = a[7] = 6; a[8] = 7; for (n=9, #a, a[n] = a[n-a[n-1]] + a[n-a[n-2]] + a[n-a[n-3]] + a[n-a[n-4]]); print (a)