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A186239 G.f. A(x) satisfies A(x) = 1+x*A(x)+x^2*A(x)^2+2*x^3*A(x)^3. 0
1, 1, 2, 6, 17, 51, 163, 533, 1779, 6055, 20908, 73052, 257863, 918139, 3293538, 11891778, 43183835, 157616827, 577902846, 2127539802, 7861397403, 29145629141, 108385383175, 404184619545, 1511132059333, 5663069529201, 21269203639596, 80044555061812 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = 1/n * sum(j=0..n, C(n,j) * sum(i=j..n+j-1, C(j,i-j) * C(n-j,3*j-n-i-1) * 2^(3*j-n-i-1))), n>0.
Conjecture: 4*(2*n+3)*(n+1)*a(n) +(113*n^2-91*n-72)*a(n-1) + 3*(-135*n^2+263*n-108)*a(n-2) -3*(107*n-119)*(n-2)*a(n-3) -1411*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 14 2011
a(n) is the top left term of M^n, M = an infinite matrix with (1,1,1,...) as diagonals starting at positions (1,2), (1,1), and (2,1); with a diagonal of (2,2,2,...) starting at (3,1). - Gary W. Adamson, Nov 25 2011
EXAMPLE
a(3) = 6 since the top row of M^3 = (6, 5, 3, 1, 0, 0, ...).
MATHEMATICA
terms = 28;
A[_] = 0;
Do[A[x_] = 1 + x A[x] + x^2 A[x]^2 + 2 x^3 A[x]^3 + O[x]^terms, {terms}];
CoefficientList[A[x], x] (* Jean-François Alcover, Aug 08 2018 *)
CROSSREFS
Sequence in context: A157002 A071717 A181665 * A148451 A148452 A307975
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Feb 15 2011
STATUS
approved

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Last modified July 23 10:53 EDT 2024. Contains 374549 sequences. (Running on oeis4.)