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 A275691 G.f. A(x) satisfies: 1 = ...(((((A(x) - x^2)^(1/2) - x^3)^(1/2) - x^4)^(1/2) - x^5)^(1/2) - x^6)^(1/2) -...- x^n)^(1/2) -..., an infinite series of nested square roots. 2
 1, 0, 1, 2, 4, 8, 17, 36, 78, 168, 364, 786, 1700, 3668, 7916, 17056, 36729, 78996, 169772, 364472, 781814, 1675464, 3587660, 7675722, 16409240, 35052552, 74822496, 159599700, 340199178, 724675528, 1542673868, 3281957116, 6977971852, 14827596904, 31489490296, 66837617960, 141789447876, 300636048724, 637116434912, 1349532001896, 2857195771769, 6046370298448 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Compare definition with that of A274965. LINKS Table of n, a(n) for n=0..41. FORMULA G.f.: A(x) = G(x,x), where G(x,y) = x*y + G(x,x*y)^2 is the g.f. of A275670. G.f.: A(x) = sqrt(F(x) - x), where F(x) is the g.f. of A274965. EXAMPLE G.f.: A(x) = 1 + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 36*x^7 + 78*x^8 + 168*x^9 + 364*x^10 + 786*x^11 + 1700*x^12 + 3668*x^13 + 7916*x^14 +... The g.f. of related sequence A274965 begins: A(x)^2 + x = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 46*x^6 + 104*x^7 + 238*x^8 + 540*x^9 + 1228*x^10 + 2780*x^11 + 6289*x^12 +... PROG (PARI) {a(n) = my(A=1 +x*O(x^n)); for(k=0, n, A = A^2 + x^(n+2-k)); polcoeff(A, n)} for(n=0, 60, print1(a(n), ", ")) CROSSREFS Cf. A274965. Antidiagonal sums of triangle A275670. Sequence in context: A063457 A262735 A190162 * A251691 A157904 A182901 Adjacent sequences: A275688 A275689 A275690 * A275692 A275693 A275694 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 05 2016 STATUS approved

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Last modified September 23 09:36 EDT 2023. Contains 365544 sequences. (Running on oeis4.)