A092687 First column and main diagonal of triangle A092686, in which the convolution of each row with {1,2} produces a triangle that, when flattened, equals the flattened form of A092686.
1, 2, 6, 16, 46, 132, 384, 1120, 3278, 9612, 28236, 83072, 244752, 722048, 2132704, 6306304, 18666190, 55300732, 163968612, 486528288, 1444571068, 4291629384, 12756459936, 37934818112, 112855778768, 335867740704, 999895548736
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..850
Programs
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Mathematica
m = 27; A[] = 1; Do[A[x] = A[x^2/(1-2x)]/(1-2x) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Nov 03 2019 *)
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PARI
T(n,k)=if(n<0||k>n,0, if(n==0&k==0,1, if(n==1&k<=1,2, if(k==n,T(n,0), 2*T(n-1,k)+T(n-1,k+1))))) a(n)=T(n,0) for(n=0,30,print1(a(n),", "))
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PARI
a(n)=local(A=1+x);for(i=0,n\2,A=subst(A,x,x^2/(1-2*x+x*O(x^n)))/(1-2*x));polcoeff(A,n) \\ Paul D. Hanna, Jul 10 2006
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PARI
/* Using Recurrence: */ a(n)=if(n==0, 1, sum(k=0, n\2, binomial(n-k, k)*2^(n-2*k)*a(k))) for(n=0,30,print1(a(n),", ")) \\ Paul D. Hanna, Jul 10 2006
Formula
G.f. satisfies: A(x) = A( x^2/(1-2x) )/(1-2x). Recurrence: a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*2^(n-2k)*a(k). - Paul D. Hanna, Jul 10 2006
Comments