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A195850
Column 6 of array A195825. Also column 1 of triangle A195840. Also 1 together with the row sums of triangle A195840.
14
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
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
(GW-BASIC)' 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
50 'Omar E. Pol, Jun 10 2012
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 07 2011
STATUS
approved