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A180712 Self-convolution of A180711. 2
1, 2, 3, 6, 11, 18, 28, 42, 61, 88, 124, 168, 227, 302, 394, 510, 653, 826, 1037, 1290, 1591, 1952, 2378, 2876, 3461, 4144, 4935, 5850, 6905, 8114, 9500, 11080, 12875, 14914, 17218, 19816, 22740, 26024, 29703, 33812, 38395, 43500, 49170, 55460 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Paul D. Hanna, Table of n, a(n), n = 0..500.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 3*x^2 + 6*x^3 + 11*x^4 + 18*x^5 + 28*x^6 +...

The square-root of the g.f. begins:

sqrt(A(x)) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6 + 6*x^7 + 7*x^8 + 9*x^9 + 11*x^10 + 12*x^11 + 15*x^12 + 17*x^13 + 19*x^14 +...

The integer part of the square-root of the coefficients of g.f. A(x) equals the respective coefficients of sqrt(A(x)), as illustrated by:

[sqrt(1)]=1; [sqrt(2)]=1; [sqrt(3)]=1; [sqrt(6)]=2; [sqrt(11)]=3;

[sqrt(18)]=4; [sqrt(28)]=5; [sqrt(42)]=6; [sqrt(61)]=7; [sqrt(88)]=9;

[sqrt(124)]=11; [sqrt(168)]=12; [sqrt(227)]=15; [sqrt(302)]=17; ...

PROG

(PARI) {a(n)=local(A=[1, 1, 1, t], T); for(i=1, n-2, for(N=A[ #A-1], 2*A[ #A-1], T=subst(Vec(Ser(A)^2)[ #A], t, N); if(sqrtint(T)==N, A[ #A]=N; A=concat(A, t); break))); Vec(Ser(A)^2)[n+1]}

CROSSREFS

Cf. A180711.

Sequence in context: A059100 A131512 A147388 * A273225 A274621 A291725

Adjacent sequences:  A180709 A180710 A180711 * A180713 A180714 A180715

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 22 2010

STATUS

approved

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Last modified February 17 20:22 EST 2018. Contains 299296 sequences. (Running on oeis4.)