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A195852
Column 8 of array A195825. Also column 1 of triangle A195842. Also 1 together with the row sums of triangle A195842.
13
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, 21, 27, 32, 34, 35, 35, 35, 36, 38, 44, 54, 67, 77, 83, 85, 86, 87, 89, 95, 107, 128, 152, 173, 185, 191, 194, 197, 203, 216, 242, 281, 328, 367, 393, 407
OFFSET
0,10
COMMENTS
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
Number of partitions of n into parts congruent to 0, 1 or 9 (mod 10). - Peter Bala, Dec 10 2020
FORMULA
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
a(n) ~ exp(Pi*sqrt(n/5))/(2*(sqrt(5)-1)*n). - Vaclav Kotesovec, Aug 14 2017
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
PROG
(GW-BASIC)' A program with two A-numbers:
10 Dim A195162(100), A057077(100), a(100): a(0)=1
20 For n = 1 to 64: For j = 1 to n
30 If A195162(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A195162(j))
40 Next j: Print a(n-1); : Next n
50 'Omar E. Pol, Jun 10 2012
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 07 2011
EXTENSIONS
More terms from Omar E. Pol, Jun 10 2012
STATUS
approved