A348862 -id:A348862

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A348860

G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(2*x))).

+10
3

1, 0, 1, 4, 37, 632, 20905, 1359692, 175426573, 45086173824, 23129393794129, 23707675064224020, 48577049664823958389, 199020196349510773741576, 1630572517436087330046884473, 26716930897552073378560239594588, 875487110213852689248519499248558685

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = (-1)^n + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1).

a(n) ~ c * 2^(n*(n-1)/2), where c = 0.658663398267275680037834076118178644268023291808559507713140088111498143... - Vaclav Kotesovec, Nov 02 2021

MATHEMATICA

nmax = 16; A[_] = 0; Do[A[x_] = 1/((1 + x) (1 - x A[2 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[n_] := a[n] = (-1)^n + Sum[2^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

CROSSREFS

Cf. A005043, A015083, A348861, A348862.

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 02 2021

STATUS

approved

A348861

G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(3*x))).

+10
2

1, 0, 1, 9, 253, 20754, 5064301, 3696964686, 8088964208893, 53079786931826952, 1044822534120774924517, 61696770693051062357722413, 10929459535778338593167921597497, 5808373834674826377471903826388912406, 9260429805605038398327449254849233420999649

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = (-1)^n + Sum_{k=0..n-1} 3^k * a(k) * a(n-k-1).

a(n) ~ c * 3^(n*(n-1)/2), where c = 0.353669086629957226916356822657293915192042094460583129054709983118948... - Vaclav Kotesovec, Nov 02 2021

MATHEMATICA

nmax = 14; A[_] = 0; Do[A[x_] = 1/((1 + x) (1 - x A[3 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[n_] := a[n] = (-1)^n + Sum[3^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]