A023436 -id:A023436 - cp's OEIS frontend

A107065 Riordan array (1/(1-x),x(1+x+x^2+x^3)).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 10, 10, 5, 1, 1, 4, 13, 20, 15, 6, 1, 1, 4, 15, 32, 35, 21, 7, 1, 1, 4, 16, 44, 66, 56, 28, 8, 1, 1, 4, 16, 54, 106, 121, 84, 36, 9, 1, 1, 4, 16, 60, 150, 222, 204, 120, 45, 10, 1, 1, 4, 16, 63, 190, 357, 420, 323, 165, 55, 11, 1, 1, 4, 16

Offset: 0

Paul Barry, May 10 2005

Row sums are A107066. Diagonal sums are A023436(n+1).

			Triangle begins
  1;
  1, 1;
  1, 2, 1;
  1, 3, 3, 1;
  1, 4, 6, 4, 1;
  1, 4, 10, 10, 5, 1;
  1, 4, 13, 20, 15, 6, 1;
  ...

Cf. A107066, A023436.

A171997 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2) - floor(a(n-5)/2); initial terms are 1, 1, 2, 3, 4.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 24, 29, 35, 42, 50, 59, 70, 83, 97, 114, 134, 156, 182, 212, 246, 285, 330, 382, 441, 509, 588, 678, 781, 900, 1037, 1193, 1373, 1580, 1817, 2089, 2402, 2761, 3172, 3645, 4187, 4809, 5523, 6342, 7282, 8360

Offset: 1

Roger L. Bagula, Nov 22 2010

nonn

lim_{n -> infinity} a(n+1)/a(n) = 1.14710876512065387719410850648860644150605499412513....

a(n) = A062435(n+2) for n < 15.

Cf. A062435 (integer part of log(n!)^log(log(1 + n))), A023434 (a(n)=a(n-1)+a(n-2)-a(n-4)), A023435 (a(n)=a(n-1)+a(n-2)-a(n-5)), A023436 (a(n)=a(n-1)+a(n-2)-a(n-6)), A023437 (a(n)=a(n-1)+a(n-2)-a(n-7)), A023438 (a(n)=a(n-1)+a(n-2)-a(n-8)), A023439 (a(n)=a(n-1)+a(n-2)-a(n-9)), A023440 (a(n)=a(n-1)+a(n-2)+a(n-10)), A023441 (a(n)=a(n-1)+a(n-2)-a(n-11)), A023442 (a(n)=a(n-1)+a(n-2)-a(n-12)), A000044 (a(n)=a(n-1)+a(n-2)-a(n-13)), A173199 (a(n)=a(n-1)+a(n-2)-floor(a(n-3)/2)-floor(a(n-8)/2)).

I:=[1,1,2,3,4]; [n le 5 select I[n] else Self(n-1) + Self(n-2) - Floor(Self(n-2)/2) - Floor(Self(n-5)/2): n in [1..60]]; // Vincenzo Librandi, Jun 24 2015

f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 2]/2] - Floor[f[n - 5]/2]
Table[f[n], {n, 0, 50}]

Offset changed from 0 to 1 by Klaus Brockhaus, Nov 29 2010

cp's OEIS Frontend

A107065 Riordan array (1/(1-x),x(1+x+x^2+x^3)).

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A171997 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2) - floor(a(n-5)/2); initial terms are 1, 1, 2, 3, 4.

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