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 A182153 G.f.: [Sum_{n>=0} x^(n^2) * (1+x+x^2)^n ]^2. 2

%I

%S 1,2,3,4,5,8,13,16,17,18,24,38,53,62,64,68,83,108,135,158,181,214,264,

%T 326,383,412,408,402,457,620,871,1124,1285,1326,1292,1266,1322,1524,

%U 1920,2504,3165,3696,3916,3818,3644,3772,4492,5796,7363,8748,9643,10014,10031

%N G.f.: [Sum_{n>=0} x^(n^2) * (1+x+x^2)^n ]^2.

%C Equals the self-convolution of the flattened triangle of trinomial coefficients (A027907).

%H Paul D. Hanna, <a href="/A182153/b182153.txt">Table of n, a(n) for n = 0..1024</a>

%F G.f.: [Sum_{n>=0} (1+x+x^2)^n*x^n * Product_{k=1..n} (1 - (1+x+x^2)*x^(4*k-3))/(1 - (1+x+x^2)*x^(4*k-1)) ]^2.

%e G.f.: A(x) = 1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 8*x^5 + 13*x^6 + 16*x^7 + 17*x^8 + 18*x^9 +...

%e such that

%e A(x)^(1/2) = 1 + x*(1+x+x^2) + x^4*(1+x+x^2)^2 + x^9*(1+x+x^2)^3 + x^16*(1+x+x^2)^4 +...

%o (PARI) {a(n)=local(A=sum(m=0, sqrtint(n+1), x^(m^2)*(1+x+x^2+x*O(x^n))^m)); polcoeff(A^2, n)}

%o for(n=0, 66, print1(a(n), ", "))

%Y Cf. A152037, A027907.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 18 2012

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Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)