A180712 Self-convolution of A180711.

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

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