A242574 a(n) = [x^n] G(n,x) where G(n,x) is the n-th iteration of G(1,x) = x/(1-x+x^2), so that G(n,x) = G(n-1, G(1,x)) with G(0,x)=x.
1, 2, 6, 26, 155, 1225, 12411, 156416, 2388060, 43159172, 905135396, 21655104900, 582527203011, 17404200037095, 571581950390602, 20454815744801708, 791762421402479311, 32941802599154381634, 1465274545936840236164, 69358520116965601147778
Offset: 1
Keywords
Examples
Given x/(1-x+x^2) = x + x^2 - x^4 - x^5 + x^7 + x^8 - x^10 - x^11 + x^13 +... form a table of coefficients in the iterations of x/(1-x+x^2) like so: [1, 1, 0, -1, -1, 0, 1, 1, 0, -1, ...]; [1, 2, 2, -1, -8, -15, -10, 22, 79, 112, ...]; [1, 3, 6, 6, -11, -73, -201, -309, 37, 1913, ...]; [1, 4, 12, 26, 24, -116, -808, -3000, -7566, -9882, ...]; [1, 5, 20, 65, 155, 120, -1379, -10761, -51202, -183269, ...]; [1, 6, 30, 129, 464, 1225, 702, -18978, -169139, -994138, ...]; [1, 7, 42, 224, 1057, 4235, 12411, 4445, -301321, -3076795, ...]; [1, 8, 56, 356, 2064, 10752, 48000, 156416, 27812, -5458012, ...]; [1, 9, 72, 531, 3639, 23064, 132633, 658197, 2388060, 187911, ...]; [1, 10, 90, 755, 5960, 44265, 306742, 1942198, 10676571, 43159172, ...]; ... then this sequence forms the main diagonal in the above table.
Links
- Paul D. Hanna, Table of n, a(n) for n = 1..200
Programs
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PARI
{a(n)=local(A=x, G=x/(1-x+x^2)); for(i=1, n, A=subst(G, x, A+x*O(x^(n)))); polcoeff(A, n)} for(n=1,30,print1(a(n),", "))