A195053 Parity of the spt function, A092269.

1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1

Offset

1

Comments

It appears that this is also the parity of A195052.

It appears that this is also the parity of the absolute values of A003475.

It appears that this is also the parity of A195012. - Omar E. Pol, May 25 2012

Links

Table of n, a(n) for n=1..86.

G. E. Andrews, The number of smallest parts in the partitions of n, J. fur Reine Angew. Math, Vol. 2008 (Issue 624), pp. 133-142.

G. E. Andrews, S. H. G. Chan, and B. Kim, The odd moments of ranks and cranks, JCT(A) 120:77-91 (2013).

G. E. Andrews, F. G. Garvan, and J. Liang, Combinatorial interpretation of congruences for the spt-function, Ramanujan Journal 29, 321-338 (2012). See also.

G. E. Andrews, F. G. Garvan, and J. Liang, Self-conjugate vector partitions and the parity of the spt-function, Acta Arithmetica 158 (2013), 199-218.

A. Folsom and K. Ono, The spt-function of Andrews, PNAS, Vol. 105, No. 51.

Formula

a(n) = A000035(A092269(n)). - Omar E. Pol, Aug 06 2013

Crossrefs

Cf. A003475, A040051, A092269, A115995, A183010, A183011, A195012, A195051, A195052, A209616.

Sequence in context: A266978 A074201 A143466 * A267136 A117908 A115360

Adjacent sequences: A195050 A195051 A195052 * A195054 A195055 A195056

Keyword

nonn

Author

Omar E. Pol, Jan 13 2012

Status

approved