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A084077 Length of list created by n substitutions k -> Range[ -Abs[k+1], Abs[k-1]] starting with {1}. 1
1, 3, 11, 41, 159, 633, 2575, 10657, 44735, 190017, 815231, 3527681, 15378687, 67478401, 297777407, 1320753665, 5884652543, 26326301697, 118211192831, 532574203905, 2406726828031, 10906541371393 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

invOGF satisfies n+(-1-3 n) a[n]+(-2 n-2 n^2) a[n]^2-2 n^2 a[n]^3 = 0

Recurrence: (n+3)*(7*n-4)*a(n) = 3*(7*n^2+3*n+2)*a(n-1) + 2*(28*n^2+5*n-9)*a(n-2) + 4*(n-1)*(7*n+3)*a(n-3). - Vaclav Kotesovec, Oct 14 2012

a(n) ~ sqrt(52+34*sqrt(2))*(2+2*sqrt(2))^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 14 2012

EXAMPLE

{1}, {-2,-1,0}, {-1,0,1,2,3,0,1,2,-1,0,1}

MATHEMATICA

Length/@Flatten/@NestList[ # /. k_Integer:>Range[ -Abs[k+1], Abs[k-1]]&, {1}, 8]

Flatten[{1, RecurrenceTable[{(n+3)*(7*n-4)*a[n] == 3*(7*n^2+3*n+2)*a[n-1] + 2*(28*n^2+5*n-9)*a[n-2] + 4*(n-1)*(7*n+3)*a[n-3], a[1]==3, a[2]==11, a[3]==41}, a, {n, 20}]}] (* Vaclav Kotesovec, Oct 14 2012 *)

CROSSREFS

Sequence in context: A258471 A176085 A129637 * A027103 A151086 A151087

Adjacent sequences:  A084074 A084075 A084076 * A084078 A084079 A084080

KEYWORD

nonn

AUTHOR

Wouter Meeussen, May 11 2003

STATUS

approved

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Last modified October 16 06:10 EDT 2019. Contains 328046 sequences. (Running on oeis4.)