cp's OEIS Frontend

A211609 12 times the total number of smallest parts in all partitions of n, with a(0) = 0.

%I A211609 #41 Aug 09 2020 07:26:04
%S A211609 0,12,36,60,120,168,312,420,684,960,1428,1932,2856,3780,5280,7068,
%T A211609 9612,12576,16884,21840,28788,37044,47976,61104,78540,99156,125832,
%U A211609 157980,198744,247560,309276,382764,474552,584304,719520,881076,1079244,1314636,1601268,1942080,2354016,2842116
%N A211609 12 times the total number of smallest parts in all partitions of n, with a(0) = 0.
%C A211609 The product 12spt(n) appears in the formula b(n) = 12spt(n)+(24n-1)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).
%C A211609 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 Dabholkar-Murthy-Zagier 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?
%H A211609 Atish Dabholkar, Sameer Murthy, Don Zagier, <a href="http://arxiv.org/abs/1208.4074">Quantum Black Holes, Wall Crossing, and Mock Modular Forms</a>, arXiv:1208.4074 [hep-th], 2012-2014.
%H A211609 F. G. Garvan, <a href="https://qseries.org/fgarvan/papers/spt2.pdf">Congruences for Andrews' spt-function modulo powers of 5, 7 and 13</a>
%H A211609 F. G. Garvan, <a href="http://arxiv.org/abs/1011.1957">Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences</a>, arXiv:1011.1957 [math.NT], 2010, see (1.5), (2.12).
%H A211609 F. G. Garvan, <a href="https://carma.newcastle.edu.au/meetings/alfcon/pdfs/Frank_Garvan-alfcon.pdf">The smallest parts partition function</a>, slides, 2012
%H A211609 Ken Ono, <a href="http://dx.doi.org/10.1073/pnas.1015339107">Congruences for the Andrews spt-function</a>, PNAS January 11, 2011 108 (2) 473-476.
%F A211609 a(n) = A220481(n) - A183011(n).
%F A211609 a(n) = 12spt(n) = 12*A092269(n) = 6(M_2(n) - N_2(n)) = 6*A211982(n) = 6*(A220909(n) - A220908(n)), n >= 1.
%Y A211609 Cf. A000041, A092269, A183010, A183011, A211982, A220481, A220908, A220909.
%K A211609 nonn
%O A211609 0,2
%A A211609 _Omar E. Pol_, Feb 16 2013