A195850 Column 6 of array A195825. Also column 1 of triangle A195840. Also 1 together with the row sums of triangle A195840.

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 5, 7, 10, 12, 13, 13, 13, 14, 16, 21, 27, 32, 34, 35, 36, 38, 44, 54, 67, 77, 83, 86, 89, 95, 107, 128, 152, 173, 186, 194, 202, 216, 242, 281, 328, 368, 396, 415, 434, 464, 514, 588, 672, 748, 803, 844

Offset

0,8

Comments

Note that this sequence contains three plateaus: [1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4], [13, 13, 13]. 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 7 (mod 8). - Peter Bala, Dec 10 2020

Links

Table of n, a(n) for n=0..59.

Formula

G.f.: Product_{k>=1} 1/((1 - x^(8*k))*(1 - x^(8*k-1))*(1 - x^(8*k-7))). - Ilya Gutkovskiy, Aug 13 2017

a(n) ~ exp(Pi*sqrt(n)/2) / (4*sqrt(2-sqrt(2))*n). - Vaclav Kotesovec, Aug 14 2017

a(n) = a(n-1) + a(n-7) - a(n-10) - a(n-22) + + - - (with the convention a(n) = 0 for negative n), where 1, 7, 10, 22, ... is the sequence of generalized 10-gonal numbers A074377. - Peter Bala, Dec 10 2020

Prog

(GWbasic)' A program with two A-numbers:
10 Dim A074377(100), A057077(100), a(100): a(0)=1
20 For n = 1 to 60: For j = 1 to n
30 If A074377(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A074377(j))
40 Next j: Print a(n-1); : Next n
' Omar E. Pol, Jun 10 2012

Crossrefs

Cf. A000041, A001082, A006950, A036820, A057077, A074377, A195825, A195830, A195848, A195849, A195851, A195852, A196933, A210964, A211971.

Sequence in context: A120510 A029117 A308547 * A253593 A174901 A308411

Adjacent sequences: A195847 A195848 A195849 * A195851 A195852 A195853

Keyword

nonn,easy

Author

Omar E. Pol, Oct 07 2011

Status

approved