A106221 Self-convolution 4th power equals A106220, which consists entirely of digits {0,1,2,3} after the initial terms {1,4}.

1, 1, -1, 2, -4, 10, -26, 71, -199, 569, -1652, 4855, -14413, 43153, -130143, 394967, -1205268, 3695771, -11381215, 35183209, -109138163, 339599993, -1059702401, 3315256789, -10396158911, 32671424776, -102879610571, 324557399534, -1025643986057, 3246330348415, -10290418283163

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Formula

Limit a(n+1)/a(n) = -3.30697774878897620974321728382452592372871...

Example

A(x) = 1 + x - x^2 + 2*x^3 - 4*x^4 + 10*x^5 - 26*x^6 + 71*x^7 -+...
A(x)^4 = 1 + 4*x + 2*x^2 + 3*x^4 + 2*x^6 + x^8 + 2*x^14 +...
A106220 = {1,4,2,0,3,0,2,0,1,0,0,0,0,0,2,0,0,0,2,...}.

Prog

(PARI) {a(n)=local(A=1+4*x); if(n==0, 1, for(j=1, n, for(k=0, 3, t=polcoeff((A+k*x^j+x*O(x^j))^(1/4), j); if(denominator(t)==1, A=A+k*x^j; break))); return(polcoeff((A+x*O(x^n))^(1/4), n)))}

Crossrefs

Cf. A106220, A106219, A106223, A106225.

Sequence in context: A257520 A035079 A259206 * A149811 A149812 A149813

Adjacent sequences: A106218 A106219 A106220 * A106222 A106223 A106224

Keyword

sign,base

Author

Paul D. Hanna, May 01 2005

Status

approved