A195852 Column 8 of array A195825. Also column 1 of triangle A195842. Also 1 together with the row sums of triangle A195842.

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

Links

Table of n, a(n) for n=0..63.

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

Crossrefs

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

Sequence in context: A196933 A102678 A029132 * A122815 A316942 A029127

Adjacent sequences: A195849 A195850 A195851 * A195853 A195854 A195855

Keyword

nonn,easy

Author

Omar E. Pol, Oct 07 2011

Extensions

More terms from Omar E. Pol, Jun 10 2012

Status

approved