A091522 Graham-Pollak sequence with initial term 5.

5, 7, 10, 14, 20, 28, 40, 57, 81, 115, 163, 231, 327, 463, 655, 927, 1311, 1854, 2622, 3708, 5244, 7416, 10488, 14832, 20976, 29665, 41953, 59331, 83907, 118663, 167815, 237326, 335630, 474653, 671261, 949307, 1342523, 1898614, 2685046

Offset: 1

Author

Eric W. Weisstein, Jan 18 2004

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..500
• Th. Stoll, On Families of Nonlinear Recurrences Related to Digits, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.2.
• Eric Weisstein's World of Mathematics, Graham-Pollak Sequence

Crossrefs

Cf. A001521, A091523.

Programs

Mathematica

NestList[Floor[Sqrt[2](#+1/2)]&,5,40] (* Harvey P. Dale, Feb 24 2018 *)

PARI

first(n)=my(v=vector(n)); v[1]=5; for(k=2,n, v[k]=sqrtint(2*(v[k-1]+1)*v[k-1])); v \\ Charles R Greathouse IV, Jan 23 2020

Formula

a(n) = floor(sqrt(2) * (a(n-1) + 1/2)).