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.

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

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