A132174 Index of starting position of n-th generation of terms in A063882.

1, 5, 10, 21, 44, 92, 189, 385, 778, 1565, 3141, 6294, 12602, 25219, 50454, 100926, 201871, 403763, 807548, 1615119, 3230263, 6460552, 12921132, 25842293, 51684616, 103369264, 206738561, 413477157, 826954350, 1653908737, 3307817513, 6615635066, 13231270174

Offset: 1

Author

N. J. A. Sloane, Nov 07 2007

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1002
• B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
• Index entries for Hofstadter-type sequences
• Index entries for linear recurrences with constant coefficients, signature (3, -2, 0, 0, 1, -3, 2).

Programs

Python

from _future_ import division
def A132174(n):
    if n == 1:
        return 1
    if n == 2:
        return 5
    h, m = divmod(n - 3, 5)
    return (382*2**(5*h + m)-10*2**m)//31- 7*h - m -(1 if m==3 else (-1 if m==4 else 2)) # Chai Wah Wu, May 17 2017

Formula

From Chai Wah Wu, May 17 2017: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-5) - 3*a(n-6) + 2*a(n-7) for n > 8.

G.f.: x*(-5*x^7 + x^6 - x^5 - x^4 - x^3 + 3*x^2 - 2*x - 1)/((x - 1)^2*(2*x - 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

Extensions

More terms from Chai Wah Wu, May 17 2017