%I #44 May 17 2024 15:24:14

%S 1,1,1,1,1,1,1,1,1,2,3,4,4,4,4,4,4,4,5,7,10,12,13,13,13,13,13,14,16,

%T 21,27,32,34,35,35,35,36,38,44,54,67,77,83,85,86,87,89,95,107,128,152,

%U 173,185,191,194,197,203,216,242,281,328,367,393,407

%N Column 8 of array A195825. Also column 1 of triangle A195842. Also 1 together with the row sums of triangle A195842.

%C Note that this sequence contains four plateaus: [1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4], [13, 13, 13, 13, 13], [35, 35, 35]. For more information see A210843 and other sequences of this family. - _Omar E. Pol_, Jun 29 2012

%C Number of partitions of n into parts congruent to 0, 1 or 9 (mod 10). - _Peter Bala_, Dec 10 2020

%F G.f.: Product_{k>=1} 1/((1 - x^(10*k))*(1 - x^(10*k-1))*(1 - x^(10*k-9))). - _Ilya Gutkovskiy_, Aug 13 2017

%F a(n) ~ exp(Pi*sqrt(n/5))/(2*(sqrt(5)-1)*n). - _Vaclav Kotesovec_, Aug 14 2017

%F a(n) = a(n-1) + a(n-9) - a(n-12) - a(n-28) + + - - (with the convention a(n) = 0 for negative n), where 1, 9, 12, 28, ... is the sequence of generalized 12-gonal numbers A195162. - _Peter Bala_, Dec 10 2020

%o (GW-BASIC)' A program with two A-numbers:

%o 10 Dim A195162(100), A057077(100), a(100): a(0)=1

%o 20 For n = 1 to 64: For j = 1 to n

%o 30 If A195162(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A195162(j))

%o 40 Next j: Print a(n-1); : Next n

%o 50 '_Omar E. Pol_, Jun 10 2012

%Y Cf. A000041, A001082, A006950, A036820, A057077, A195162, A195825, A195832, A195848, A195849, A195850, A195851, A196933, A210964, A211971.

%K nonn,easy

%O 0,10

%A _Omar E. Pol_, Oct 07 2011

%E More terms from _Omar E. Pol_, Jun 10 2012