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A083353 Coefficients of power series A(x) consist entirely of squares, where A(x) = A083352(x)^2 + A083352(x) - 1. 3
1, 9, 36, 81, 144, 225, 324, 576, 1089, 1296, 1764, 2916, 4356, 6084, 7569, 9801, 16641, 20736, 25281, 32400, 39204, 53361, 69696, 76176, 90000, 110889, 149769, 176400, 184041, 207936, 281961, 338724, 363609, 349281, 455625, 540225, 665856, 772641, 746496, 893025, 1258884, 1375929, 1565001, 1587600, 1782225, 2259009, 2576025, 2722500, 2985984, 3186225, 3837681, 4284900, 4928400, 5143824, 5475600, 6320196, 7290000, 8311689, 8520561, 8803089 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

After the first term, all terms seem to be a multiples of 9.

LINKS

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

EXAMPLE

G.f.: A(x) = 1 + 9*x + 36*x^2 + 81*x^3 + 144*x^4 + 225*x^5 + 324*x^6 + 576*x^7 + 1089*x^8 + 1296*x^9 + 1764*x^10 + 2916*x^11 + 4356*x^12 + 6084*x^13 + 7569*x^14 + 9801*x^15 + 16641*x^16 + 20736*x^17 + 25281*x^18 + 32400*x^19 + 39204*x^20 + 53361*x^21 + 69696*x^22 + 76176*x^23 + 90000*x^24 + 110889*x^25 + 149769*x^26 + 176400*x^27 + 184041*x^28 + 207936*x^29 + 281961*x^30 + ...

where A(x) = B(x)^2 + B(x) - 1 with B(x) the g.f. of A083352, which begins:

B(x) = 1 + 3*x + 9*x^2 + 9*x^3 + 3*x^4 + 15*x^5 + 33*x^6 + 18*x^7 + 36*x^8 + 24*x^9 + 75*x^10 + 96*x^11 + 51*x^12 + 96*x^13 + 159*x^14 + 165*x^15 + 255*x^16 + 168*x^17 + 27*x^18 + 60*x^19 + 333*x^20 + 255*x^21 + 66*x^22 + 18*x^23 + 441*x^24 + 291*x^25 + 735*x^26 + 258*x^27 + 390*x^28 + 696*x^29 + 480*x^30 + ...

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(B[#B], ", "); A0[#A0]=n; A=A0; break)))); B}

CROSSREFS

Cf. A083352, A083354 (square root of terms).

Sequence in context: A073946 A016766 A242538 * A083014 A202287 A001487

Adjacent sequences:  A083350 A083351 A083352 * A083354 A083355 A083356

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 November 13 17:34 EST 2019. Contains 329106 sequences. (Running on oeis4.)