A135688 a(n) = A004001(n)*a(n-1) + a(n-2), for n > 2, with a(1) = a(2) = 1.

1, 1, 3, 7, 24, 103, 436, 1847, 9671, 59873, 428782, 3061347, 24919558, 202417811, 1644262046, 13356514179, 121852889657, 1231885410749, 13672592407896, 165302994305501, 1997308524073908, 26130313807266305, 367821701825802178

Offset: 1

Author

Roger L. Bagula, Feb 19 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A004001, A174232.

Programs

Mathematica

HC[n_]:= HC[n]= If[n<3, Fibonacci[n], HC[HC[n-1]] +HC[n -HC[n-1]]]; (*A004001*)
a[n_] := a[n] = If[n<3, 1, HC[n]*a[n-1] + a[n-2]];
Table[a[n], {n, 40}]

Sage

@cached_function
def HC(n): # HC = A004001
    if (n<3): return fibonacci(n)
    else: return HC(HC(n-1)) +HC(n -HC(n-1))
@CachedFunction
def a(n): # A135688
    if (n<3): return 1
    else: return HC(n)*a(n-1) + a(n-2)
[a(n) for n in (1..40)] # G. C. Greubel, Nov 25 2021

Formula

a(n) = A004001(n)*a(n-1) + a(n-2), for n > 2, with a(1) = a(2) = 1.

Extensions

Edited and corrected by Eric M. Schmidt, Dec 21 2014