OFFSET
1,9
COMMENTS
The sums of seven successive terms give A000070. - Omar E. Pol, Jul 12 2012
a(n) is also the difference between the sum of 7th largest and the sum of 8th largest elements in all partitions of n. - Omar E. Pol, Oct 25 2012
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
David Benson, Radha Kessar, and Markus Linckelmann, Hochschild cohomology of symmetric groups in low degrees, arXiv:2204.09970 [math.GR], 2022.
FORMULA
a(n) ~ exp(Pi*sqrt(2*n/3)) / (14*Pi*sqrt(2*n)) * (1 - 85*Pi/(24*sqrt(6*n)) + (85/48 + 4873*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 05 2016
G.f.: x^7/(1 - x^7) * Product_{k>=1} 1/(1 - x^k). - Ilya Gutkovskiy, Apr 06 2017
MAPLE
b:= proc(n, i) option remember; local g;
if n=0 or i=1 then [1, 0]
else g:= `if`(i>n, [0$2], b(n-i, i));
b(n, i-1) +g +[0, `if`(i=7, g[1], 0)]
fi
end:
a:= n-> b(n, n)[2]:
seq(a(n), n=1..100); # Alois P. Heinz, Oct 27 2012
MATHEMATICA
<< DiscreteMath`Combinatorica`; Table[ Count[ Flatten[ Partitions[n]], 7], {n, 1, 52} ]
Table[Count[Flatten[IntegerPartitions[n]], 7], {n, 55}] (* Harvey P. Dale, Feb 26 2015 *)
b[n_, i_] := b[n, i] = Module[{g}, If[n == 0 || i == 1, {1, 0}, g = If[i > n, {0, 0}, b[n - i, i]]; b[n, i - 1] + g + {0, If[i == 7, g[[1]], 0]}]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 09 2015, after Alois P. Heinz *)
PROG
(PARI) x='x+O('x^50); concat([0, 0, 0, 0, 0, 0], Vec(x^7/(1 - x^7) * prod(k=1, 50, 1/(1 - x^k)))) \\ Indranil Ghosh, Apr 06 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved