The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A177395 G.f. satisfies: x = A(x) - A(A(x))^2 - A(A(A(x)))^3. 3
 1, 1, 5, 37, 338, 3530, 40546, 500781, 6556080, 90097535, 1290778689, 19180015667, 294460699563, 4656776745569, 75682133890995, 1261603117268148, 21537605020132685, 376060923637721700, 6708681746445946648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Paul D. Hanna, Table of n, a(n), n= 1..100. FORMULA G.f. satisfies: x = A( x - A(x)^2 - A(A(x))^3 ). ... G.f. satisfies: A_{n}(x) = A_{n+1}(x) - A_{n+2}(x)^2 - A_{n+3}(x)^3 where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x. ... Given g.f. A(x), A(x)/x is the unique solution to variable A in the infinite system of simultaneous equations starting with: . A = 1 + xB^2 + x^2*C^3; . B = A + xC^2 + x^2*D^3; . C = B + xD^2 + x^2*E^3; . D = C + xE^2 + x^2*F^3; ... . also B = A(A(x))/x, C = A(A(A(x)))/x, D = A(A(A(A(x))))/x, etc. EXAMPLE G.f.: A(x) = x + x^2 + 5*x^3 + 37*x^4 + 338*x^5 + 3530*x^6 +... Coefficients in the iterations A_{n}(x), n=1..9, of A(x) begin: A_1: [1, 1, 5, 37, 338, 3530, 40546, 500781, ...]; A_2: [1, 2, 12, 100, 998, 11197, 136682, 1780674, ...]; A_3: [1, 3, 21, 195, 2120, 25571, 332664, 4589974, ...]; A_4: [1, 4, 32, 328, 3868, 50078, 694340, 10157760, ...]; A_5: [1, 5, 45, 505, 6430, 89120, 1315126, 20388639, ...]; A_6: [1, 6, 60, 732, 10018, 148195, 2322702, 38106722, ...]; A_7: [1, 7, 77, 1015, 14868, 234017, 3886428, 67351872, ...]; A_8: [1, 8, 96, 1360, 21240, 354636, 6225480, 113733264, ...]; A_9: [1, 9, 117, 1773, 29418, 519558, 9617706, 184845297,...]. Coefficients in functions: x = A(x) - A_2(x)^2 - A_3(x)^3 begin: (A_1)^1: [1, 1, 5, 37, 338, 3530, 40546, 500781, 6556080, ...]; (A_2)^2: [0, 1, 4, 28, 248, 2540, 28786, 352104, 4576404 ...]; (A_3)^3: [0, 0, 1,. 9,. 90,. 990, 11760, 148677, 1979676, ...]. Coefficients in functions: A(x) = A_2(x) - A_3(x)^2 - A_4(x)^3 begin: (A_2)^1: [1, 2, 12, 100, 998, 11197, 136682, 1780674, 24453430, ...]; (A_3)^2: [0, 1,. 6,. 51, 516,. 5851,. 72052,. 945819, 13076714, ...]; (A_4)^3: [0, 0,. 1,. 12, 144,. 1816,. 24084,. 334074,. 4820636, ...]. Coefficients in functions: A_2(x) = A_3(x) - A_4(x)^2 -A_5(x)^3 begin: (A_3)^1: [1, 3, 21, 195, 2120, 25571, 332664, 4589974, 66441348, ...]; (A_4)^2: [0, 1,. 8,. 80,. 912, 11384, 152092, 2144440, 31612640, ...]; (A_5)^3: [0, 0,. 1,. 15,. 210,. 2990,. 43890,. 664860, 10375278, ...]. PROG (PARI) {a(n)=local(A=x); if(n<1, 0, for(i=1, n, A=serreverse(x-(A+x*O(x^n))^2-subst(A, x, A+x*O(x^n))^3)); polcoeff(A, n))} CROSSREFS Cf. A139702, A177396, A171780. Sequence in context: A199562 A246540 A365842 * A370343 A258296 A197713 Adjacent sequences: A177392 A177393 A177394 * A177396 A177397 A177398 KEYWORD nonn AUTHOR Paul D. Hanna, May 29 2010 EXTENSIONS Typos in examples corrected by Paul D. Hanna, May 29 2010 Formula corrected by Paul D. Hanna, May 29 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 25 14:04 EDT 2024. Contains 374592 sequences. (Running on oeis4.)