A117261 -id:A117261 - cp's OEIS frontend

A073587 a(n) = a(n-1)*2^n + 1 where a(0)=1.

1, 3, 13, 105, 1681, 53793, 3442753, 440672385, 112812130561, 57759810847233, 59146046307566593, 121131102837896382465, 496152997224023582576641, 4064485353259201188467843073, 66592528027798752271857140908033, 2182103958414909514444214793274425345

Offset: 0

Felice Russo, Aug 28 2002

Also, number of nodes in an n-ary tree with increasing fanout as the level increases. - Dhruv Matani, Apr 12 2012

Cf. A000225 (nodes in a binary tree).

Cf. A006125, A117261, A299998.

a = 1; Table[a = a*2^n + 1, {n, 14}] (* Jayanta Basu, Jul 02 2013 *)

25 A=1
30 for I=1 to 20
40 A=A*2^I+1
50 print A
60 next
70 end

a(n) = floor(D*2^(n*(n+1)/2)) where D is a constant, D=1.64163256065515386629... = Sum_{k>=0} 1/2^(k(k+1)/2) = A299998. - Benoit Cloitre, Sep 01 2002

Added a(0)=1. Added information from duplicate sequence A182104. - N. J. A. Sloane, Dec 28 2015

A117263 Row sums of triangle A117262; also, self-convolution of A117264.

Original entry on oeis.org

1, 2, 7, 64, 1729, 140050, 34032151, 24809438080, 54258241080961, 355988319732185122, 7006918097288599756327, 413751506726794527011353024, 73294838162131470076480154142529

Offset: 0

Paul D. Hanna, Mar 14 2006

nonn

Cf. A117261, A117262, A117264.

PARI
```
a(n)=sum(k=0,n,3^((n-k)*(n+k-1)/2))
```

a(n) = Sum_{k=0..n} 3^( n*(n-1)/2 - k*(k-1)/2 ).

G.f. A(x) satisfies: A(x) = 1/(1 - x) + x * A(3*x). - Ilya Gutkovskiy, Jun 06 2020

A335901 a(n) = 2*a(floor((n-1)/a(n-1))) with a(1) = 1.

Original entry on oeis.org

1, 2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 1

Altug Alkan, following a suggestion from Andrew R. Booker, Jun 29 2020

Least k such that a(k) = 2^n are 1, 2, 5, 21, 169, 2705, ... (Conjecture: This sequence is A117261).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A130147, A132424, A130535, A283207, A288914, A335898.

f:= proc(n) option remember;
  2*procname(floor((n-1)/procname(n-1))) end proc:
f(1):= 1:
map(f, [$1..105]); # Robert Israel, Jul 08 2020

a[1] = 1; a[n_] := a[n] = 2 * a[Floor[(n-1)/a[n-1]]]; Array[a, 100] (* Amiram Eldar, Jun 29 2020 *)

a=vector(10^3); a[1]=1; for(n=2, #a, a[n]=2*a[(n-1)\a[n-1]]); a

cp's OEIS Frontend

A073587 a(n) = a(n-1)*2^n + 1 where a(0)=1.

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A117263 Row sums of triangle A117262; also, self-convolution of A117264.

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A335901 a(n) = 2*a(floor((n-1)/a(n-1))) with a(1) = 1.

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