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A083354 Square root of coefficients of power series: A083352(x)^2 + A083352(x) - 1; term-by-term square root of A083353. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 16 16:08 EDT 2021. Contains 347473 sequences. (Running on oeis4.)