|
|
A195849
|
|
Column 5 of array A195825. Also column 1 of triangle A195839. Also 1 together with the row sums of triangle A195839.
|
|
17
|
|
|
1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 5, 7, 10, 12, 13, 13, 14, 16, 21, 27, 32, 34, 36, 38, 44, 54, 67, 77, 84, 88, 95, 107, 128, 152, 174, 188, 200, 215, 242, 281, 329, 370, 402, 428, 462, 513, 589, 674, 754, 816, 873, 940, 1041, 1176, 1333, 1477, 1600, 1710, 1845
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
COMMENTS
|
Note that this sequence contains three plateaus: [1, 1, 1, 1, 1, 1], [4, 4, 4, 4], [13, 13]. For more information see A210843. See also other columns of A195825. - Omar E. Pol, Jun 29 2012
Number of partitions of n into parts congruent to 0, 1 or 6 (mod 7). - Ludovic Schwob, Aug 05 2021
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Product_{k>=1} 1/((1 - x^(7*k))*(1 - x^(7*k-1))*(1 - x^(7*k-6))). - Ilya Gutkovskiy, Aug 13 2017
|
|
MAPLE
|
7*n^2/8+7*n/8-3/16+3*(-1)^n*(1/16+n/8) ;
end proc:
option remember;
local ks, a, j ;
0 ;
elif n <= 5 then
return 1;
elif k = 1 then
a := 0 ;
for j from 1 do
a := a+procname(n-1, j) ;
else
break;
end if;
end do;
return a;
else
(-1)^floor((k-1)/2)*procname(n-ks+1, 1) ;
end if;
end proc:
end proc:
|
|
MATHEMATICA
|
m = 61;
|
|
PROG
|
(GWbasic)' A program with two A-numbers:
20 For n = 1 to 61: For j = 1 to n
40 Next j: Print a(n-1); : Next n (End)
|
|
CROSSREFS
|
Cf. A000041, A001082, A006950, A036820, A057077, A118277, A195825, A195829, A195839, A195848, A195850, A195851, A195852, A196933, A210843, A210964, A211971.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|