0,5

Also number of partitions of n with positive crank (n>1), cf. A064391. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 30 2001

G. E. Andrews, The reasonable and unreasonable effectiveness of number theory in statistical mechanics, pp. 21-34 of S. A. Burr, ed., The Unreasonable Effectiveness of Number Theory, Proc. Sympos. Appl. Math., 46 (1992). Amer. Math. Soc.

G. E. Andrews, Three-quadrant Ferrers graphs, Indian J. Math., 42 (No. 1, 2000), 1-7.

F. C. Auluck, On some new types of partitions associated with generalized Ferrers graphs. Proc. Cambridge Philos. Soc. 47, (1951), 679-686.

E. M. Wright, Stacks, III, Quart. J. Math. Oxford, 23 (1972), 153-158.

T. D. Noe, Table of n, a(n) for n = 0..1000

Erich Friedman, Illustration of initial terms

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

G.f.: (Sum_{k>0} -(-1)^k x^(k(k+1)/2))/(Product_{k>0} (1-x^k)).

For a(6)=5 we have the following stacks:

.x... ..x.. ...x. .xx.

xxxxx xxxxx xxxxx xxxx xxxxxx

A001522:=(1-z-z**2+z**3-z**6-2*z**7+2*z**5+z**10+z**8)/(1+z)/(z**4+z**3-1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]

(PARI) a(n)=if(n<1, 0, polcoeff(sum(k=1, (sqrt(1+8*n)-1)\2, -(-1)^k*x^((k+k^2)/2))/eta(x+x*O(x^n)), n))

a(n) = (A000041(n)-A064410(n))/2.

Cf. A000041, A059776, A001523, A001524.

Adjacent sequences: A001519 A001520 A001521 this_sequence A001523 A001524 A001525

Sequence in context: A096778 A102108 A105780 this_sequence A054405 A116634 A035960

nonn,easy,nice

njas