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A125096 Expansion of -1 + (phi(q) * phi(q^2) + phi(-q^2) * phi(q^4)) / 2 in powers of q. 1
1, 0, 2, 2, 0, 0, 0, 2, 3, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 1, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, 1, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 6, 2, 0, 2, 4, 0, 0, 0, 0, 5, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 6, 2, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..105.

FORMULA

a(n) is multiplicative with a(2) = 0, a(2^e) = 2 if e>1, a(p^e) = e+1 if p == 1, 3 (mod 8), a(p^e) = (1+(-1)^e)/2 if p == 5, 7 (mod 8).

a(4*n + 2) = a(8*n + 5) = a(8*n + 7) = 0. a(4*n) = 2 * A002325(n). a(8*n + 1) = A112603(n). a(8*n + 3) = A033761(n).

PROG

(PARI) {a(n) = if( n<1, 0, qfrep([1, 0; 0, 8], n)[n] + qfrep([3, 1; 1, 3], n)[n])}

CROSSREFS

Cf. A002324, A033761, A112603.

Sequence in context: A024158 A054978 A129438 * A037862 A285244 A263148

Adjacent sequences:  A125093 A125094 A125095 * A125097 A125098 A125099

KEYWORD

nonn,mult

AUTHOR

Michael Somos, Nov 20 2006

STATUS

approved

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Last modified July 8 04:16 EDT 2020. Contains 335504 sequences. (Running on oeis4.)