A036294 -id:A036294 - cp's OEIS frontend

A064754 a(n) = n*8^n - 1.

7, 127, 1535, 16383, 163839, 1572863, 14680063, 134217727, 1207959551, 10737418239, 94489280511, 824633720831, 7146825580543, 61572651155455, 527765581332479, 4503599627370495, 38280596832649215, 324259173170675711, 2738188573441261567, 23058430092136939519

Offset: 1

N. J. A. Sloane, Oct 19 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Paul Leyland, Factors of Cullen and Woodall numbers.
Paul Leyland, Generalized Cullen and Woodall numbers.
Index entries for linear recurrences with constant coefficients, signature (17,-80,64).

Cf. A003261, A036294.

[ n*8^n-1: n in [1..20]]; // Vincenzo Librandi, Sep 16 2011

Table[n*8^n-1,{n,20}] (* or *) LinearRecurrence[{17,-80,64},{7,127,1535},20] (* Harvey P. Dale, May 20 2013 *)

G.f.: x*(64*x^2 - 8*x - 7)/((x-1)*(8*x-1)^2). - Colin Barker, Oct 15 2012
a(n) = 17*a(n-1) - 80*a(n-2) + 64*a(n-3); a(1)=7, a(2)=127, a(3)=1535. - Harvey P. Dale, May 20 2013
From Elmo R. Oliveira, May 05 2025: (Start)
E.g.f.: 1 + exp(x)*(8*x*exp(7*x) - 1).
a(n) = A036294(n) - 1. (End)

A064746 a(n) = n*8^n + 1.

Original entry on oeis.org

1, 9, 129, 1537, 16385, 163841, 1572865, 14680065, 134217729, 1207959553, 10737418241, 94489280513, 824633720833, 7146825580545, 61572651155457, 527765581332481, 4503599627370497, 38280596832649217, 324259173170675713, 2738188573441261569, 23058430092136939521

Offset: 0

N. J. A. Sloane, Oct 19 2001

Harry J. Smith, Table of n, a(n) for n = 0..150
Paul Leyland, Factors of Cullen and Woodall numbers.
Paul Leyland, Generalized Cullen and Woodall numbers.
Index entries for linear recurrences with constant coefficients, signature (17,-80,64).

Cf. A002064, A036294.

Table[n*8^n+1,{n,0,20}] (* or *) LinearRecurrence[{17,-80,64},{1,9,129},20] (* Harvey P. Dale, Jul 24 2012 *)

a(n) = { n*8^n + 1 } \\ Harry J. Smith, Sep 24 2009

a(n) = 17*a(n-1) - 80*a(n-2) + 64*a(n-3), a(0)=1, a(1)=9, a(2)=129. - Harvey P. Dale, Jul 24 2012
G.f.: -(56*x^2-8*x+1)/((x-1)*(8*x-1)^2). - Colin Barker, Oct 15 2012
From Elmo R. Oliveira, May 04 2025: (Start)
E.g.f.: exp(x)*(1 + 8*x*exp(7*x)).
a(n) = A036294(n) + 1. (End)

A158749 a(n) = n*9^n.

Original entry on oeis.org

0, 9, 162, 2187, 26244, 295245, 3188646, 33480783, 344373768, 3486784401, 34867844010, 345191655699, 3389154437772, 33044255768277, 320275094369454, 3088366981419735, 29648323021629456, 283512088894331673, 2701703435345984178, 25666182635786849691, 243153309181138576020

Offset: 0

Zerinvary Lajos, Mar 25 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (18,-81).

Cf. A001019, A018215, A036289, A036290, A036291, A036292, A036293, A036294.

Cf. A038299, A126431.

[n*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 25 2014

Table[n 9^n, {n, 0, 20}] (* Vincenzo Librandi, Feb 25 2014 *)

a(n) = n*9^n; \\ Joerg Arndt, Feb 23 2014

a(n) = n*9^n.
From R. J. Mathar, Mar 26 2009: (Start)
a(n) = 18*a(n-1) - 81*a(n-2) = A038299(n,1).
G.f.: 9*x/(1-9*x)^2. (End)
a(n) = A001019(n)*n. - Omar E. Pol, Mar 26 2009
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = log(9/8).
Sum_{n>=1} (-1)^(n+1)/a(n) = log(10/9). (End)
E.g.f.: 9*x*exp(9*x). - Elmo R. Oliveira, Sep 09 2024

A134574 Array, a(n,k) = total size of all n-length words on a k-letter alphabet, read by antidiagonals.

Original entry on oeis.org

1, 2, 2, 3, 8, 3, 4, 24, 18, 4, 5, 64, 81, 32, 5, 6, 160, 324, 192, 50, 6, 7, 384, 1215, 1024, 375, 72, 7, 8, 896, 4374, 5120, 2500, 648, 98, 8, 9, 2048, 15309, 24576, 15625, 5184, 1029, 128, 9, 10, 4608, 52488, 114688, 93750, 38880, 9604, 1536, 162, 10

Offset: 1

Ross La Haye, Jan 22 2008

			a(2,2) = 8 because there are 2^2 = 4 2-length words on a 2 letter alphabet, each of size 2 and 2*4 = 8.
Array begins:
==================================================================
n\k|  1     2       3        4         5         6          7  ...
---|--------------------------------------------------------------
1  |  1     2       3        4         5         6          7  ...
2  |  2     8      18       32        50        72         98  ...
3  |  3    24      81      192       375       648       1029  ...
4  |  4    64     324     1024      2500      5184       9604  ...
5  |  5   160    1215     5120     15625     38880      84035  ...
6  |  6   384    4374    24576     93750    279936     705894  ...
7  |  7   896   15309   114688    546875   1959552    5764801  ...
8  |  8  2048   52488   524288   3125000  13436928   46118408  ...
9  |  9  4608  177147  2359296  17578125  90699264  363182463  ...
... - _Franck Maminirina Ramaharo_, Aug 07 2018

Cf. a(n, 1) = a(1, k) = A000027(n); a(n, 2) = A036289(n); a(n, 3) = A036290(n); a(n, 4) = A018215(n); a(n, 5) = A036291(n); a(n, 6) = A036292(n); a(n, 7) = A036293(n); a(n, 8) = A036294(n); a(2, k) = A001105(k); a(3, k) = A117642(k); a(n, n) = A007778(n); a(n, n+1) = A066274(n+1): sum[a(i-1, n-i+1), {i, 1, n}] = A062807(n).

t[n_, k_] := Sum[k^n, {j, n}]; Table[ t[n - k + 1, k], {n, 10}, {k, n}] // Flatten (* Robert G. Wilson v, Aug 07 2018 *)

a(n,k) = n*k^n.
O.g.f. (by columns): (k*x)/(-1+k*x)^2.
E.g.f. (by columns): k*x*exp(k*x).
a(n,k) = Sum[k^n,{j,1,n}] = n*Sum[C(n,m)*(k-1)^m,{m,0,n}]. - Ross La Haye, Jan 26 2008

cp's OEIS Frontend

A064754 a(n) = n*8^n - 1.

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A064746 a(n) = n*8^n + 1.

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A158749 a(n) = n*9^n.

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A134574 Array, a(n,k) = total size of all n-length words on a k-letter alphabet, read by antidiagonals.

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