

A211609


12 times the total number of smallest parts in all partitions of n, with a(0) = 0.


1



0, 12, 36, 60, 120, 168, 312, 420, 684, 960, 1428, 1932, 2856, 3780, 5280, 7068, 9612, 12576, 16884, 21840, 28788, 37044, 47976, 61104, 78540, 99156, 125832, 157980, 198744, 247560, 309276, 382764, 474552, 584304, 719520, 881076, 1079244, 1314636, 1601268, 1942080, 2354016, 2842116
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OFFSET

0,2


COMMENTS

The product 12spt(n) appears in the formula b(n) = 12spt(n)+(24n1)p(n) which is mentioned in several papers (see Ono's paper, see also Garvan's papers and Garvan's slides in link section). Note that b(n) is A220481(n).
Observation: first 13 terms coincide with the differences between all terms mentioned in a table of special mock Jacobi forms and the first 13 terms of A183011. For the table see DabholkarMurthyZagier paper, appendix A.1, table of Q_M (weight 2 case), M = 6, C_M = 12. See also the table in page 46. Question: do all terms coincide?


LINKS

Table of n, a(n) for n=0..41.
Atish Dabholkar, Sameer Murthy, Don Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms
F. G. Garvan, Congruences for Andrews' sptfunction modulo powers of 5, 7 and 13
F. G. Garvan, Congruences for Andrews' sptfunction modulo 32760 and extension of Atkin's Hecketype partition congruences, see (1.5), (2.12).
F. G. Garvan, The smallest parts partition function, slides, 2012
Ken Ono, Congruences for the Andrews sptfunction


FORMULA

a(n) = A220481(n)  A183011(n).
a(n) = 12spt(n) = 12*A092269(n) = 6(M_2(n)  N_2(n)) = 6*A211982(n) = 6*(A220909(n)  A220908(n)), n >= 1.


CROSSREFS

Cf. A000041, A092269, A183010, A183011, A211982, A220481, A220908, A220909.
Sequence in context: A063298 A055926 A073762 * A043140 A043920 A049598
Adjacent sequences: A211606 A211607 A211608 * A211610 A211611 A211612


KEYWORD

nonn


AUTHOR

Omar E. Pol, Feb 16 2013


STATUS

approved



