A210964 Column 10 of square array A195825. Also column 1 of triangle A210954. Also 1 together with the row sums of triangle A210954

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 10, 12, 13, 13, 13, 13, 13, 13, 13, 14, 16, 21, 27, 32, 34, 35, 35, 35, 35, 35, 36, 38, 44, 54, 67, 77, 83, 85, 86, 86, 86, 87, 89, 95, 107, 128, 152, 173, 185, 191, 193, 194, 195

Offset

0,12

Comments

Note that this sequence contains five plateaus: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4], [13, 13, 13, 13, 13, 13, 13], [35, 35, 35, 35, 35], [86, 86, 86]. For more information see A210843 and other sequences of this family. - Omar E. Pol, Jun 29 2012

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..3000 from Vaclav Kotesovec)

Vaclav Kotesovec, Graph - The asymptotic ratio

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of 1 / f(-x, -x^11) in powers of x where f() is a Ramanujan theta function. - Michael Somos, Jan 10 2015

Partitions of n into parts of the form 12*k, 12*k+1, 12*k+11. - Michael Somos, Jan 10 2015

Euler transform of period 12 sequence [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, ...]. - Michael Somos, Jan 10 2015

G.f.: Product_{k>0} 1 / ((1 - x^(12*k)) * (1 - x^(12*k - 1)) * (1 - x^(12*k - 11))).

Convolution inverse of A247133.

a(n) ~ sqrt(2)*(1+sqrt(3)) * exp(Pi*sqrt(n/6)) / (8*n). - Vaclav Kotesovec, Nov 08 2015

a(n) = (1/n)*Sum_{k=1..n} A284372(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 25 2017

a(n) = a(n-1) + a(n-11) - a(n-14) - a(n-34) + + - - (with the convention a(n) = 0 for negative n), where 1, 11, 14, 34, ... is the sequence of generalized 14-gonal numbers A195818. - Peter Bala, Dec 10 2020

Mathematica

nmax = 100; CoefficientList[Series[Product[1 / ((1 - x^(12*k)) * (1 - x^(12*k-1)) * (1 - x^(12*k-11))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 08 2015 *)

Prog

(GWbasic)' A program with two A-numbers:
10 Dim A195818(100), A057077(100), a(100): a(0)=1
20 For n = 1 to 67: For j = 1 to n
30 If A195818(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A195818(j))
40 Next j: Print a(n-1); : Next n
50 End

Crossrefs

Cf. A000041, A006950, A036820, A057077, A195818, A195825, A195848, A195849, A195850, A195851, A195852, A196933, A210944, A210954, A211970, A211971.

Cf. A247133.

Sequence in context: A158411 A065680 A093391 * A029135 A196933 A102678

Adjacent sequences: A210961 A210962 A210963 * A210965 A210966 A210967

Keyword

nonn

Author

Omar E. Pol, Jun 16 2012

Status

approved