A083354 Square root of coefficients of power series: A083352(x)^2 + A083352(x) - 1; term-by-term square root of A083353.

1, 3, 6, 9, 12, 15, 18, 24, 33, 36, 42, 54, 66, 78, 87, 99, 129, 144, 159, 180, 198, 231, 264, 276, 300, 333, 387, 420, 429, 456, 531, 582, 603, 591, 675, 735, 816, 879, 864, 945, 1122, 1173, 1251, 1260, 1335, 1503, 1605, 1650, 1728, 1785, 1959, 2070, 2220, 2268, 2340, 2514, 2700, 2883, 2919, 2967, 3294, 3552, 3447, 3744, 3633, 4110, 4251, 4338, 4221, 4851, 4962, 5226, 5217, 5487, 5718, 6243, 6033, 6534, 6753, 6678, 7158

Offset

0,2

Comments

After the first term, each term seems to be a multiple of 3.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Formula

a(n) = sqrt(A083353(n)).

Example

A083352(x) = 1 + 3x + 9x^2 + 9x^3 + 3x^4 + 15x^5 + 33x^6 + ...; thus,
A083353(x) = A083352(x)^2 + A083352(x) - 1 = 1 + 9x + 36x^2 + 81x^3 + 144x^4 + 225x^5 + ...

Prog

(PARI) {for(i=1, 30, A=[1]; print1(1, ", "); for(i=1, 200, A0=concat(A, 0); for(n=1, 100*A[#A], A0[#A0]=n; B=Vec(Ser(A0)^2 + Ser(A0) - 1); if(issquare(B[#B]), print1(sqrtint(B[#B]), ", "); A0[#A0]=n; A=A0; break)))); C=vector(#B, n, sqrtint(B[n]))}

Crossrefs

Cf. A083352, A083353.

Sequence in context: A284601 A039004 A070021 * A156242 A060293 A336803

Adjacent sequences: A083351 A083352 A083353 * A083355 A083356 A083357

Keyword

nonn

Author

Paul D. Hanna, Apr 26 2003

Extensions

Extended by Paul D. Hanna, Nov 19 2017

Status

approved