0,2

First differences consist of duplicated terms: {1, 1, 5, 5, 23, 23, 75, 75, 242, 242, 666, 666, 1798, 1798, ...}; the convolution of these first differences results in: {1, 2, 11, 20, 81, 142, 451, 760, 2143, 3526, 8965, ...}, which in turn has first differences that consist of duplicated terms: {1, 1, 9, 9, 61, 61, 309, 309, ...}.

Let f(x) = sum_{n=0..inf} A073709(n) x^n, then f(x) satisfies f(x)^2 = sum_{n=0..inf} a(n) x^n, as well as the functional equation f(x^2)^2 = (1 - x)*f(x).

(1 +x +3x^2 +3x^3 +10x^4 +10x^5 +22x^6 +22x^7 +57x^8 +57x^9 +...)^2 = (1 +2x +7x^2 +12x^3 +35x^4 +58x^5 +133x^6 +208x^7 +450x^8 +...) and the first differences of the unique terms {1,3,10,22,57,...} is {1,2,7,12,35,...}.

Cf. A073707, A073708, A073709.

Sequence in context: A059053 A032025 A088662 this_sequence A092831 A055257 A084068

Adjacent sequences: A073707 A073708 A073709 this_sequence A073711 A073712 A073713

easy,nice,nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Aug 05 2002