A032770 -id:A032770 - cp's OEIS frontend

A032768 a(n) = floor( n(n+1)(n+2)(n+3)(n+4) / (n+(n+1)+(n+2)+(n+3)+(n+4)) ).

0, 8, 36, 100, 224, 432, 756, 1232, 1900, 2808, 4004, 5544, 7488, 9900, 12852, 16416, 20672, 25704, 31600, 38456, 46368, 55440, 65780, 77500, 90720, 105560, 122148, 140616, 161100, 183744, 208692, 236096, 266112, 298900, 334628, 373464, 415584

Offset: 0

Patrick De Geest, May 15 1998

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,1,-4,6,-4,1).

Cf. A032769, A032770.

[Floor(n*(n+1)*(n+3)*(n+4)/5): n in [0..36]]; // Bruno Berselli, Jun 20 2012

CoefficientList[Series[4*x*(1+x)*(2-x+2*x^2)/((1-x)^5*(1+x+x^2+x^3+x^4)),{x,0,40}],x] (* Vincenzo Librandi, Jun 20 2012 *)

G.f.: 4*x*(1+x)*(2-x+2*x^2)/((1-x)^5*(1+x+x^2+x^3+x^4)).

a(n) = floor( n(n+1)(n+3)(n+4)/5 ). [Bruno Berselli, Jun 20 2012]

A032769 Numbers that are congruent to {0, 1, 2, 4} mod 5.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 84, 85

Offset: 1

Patrick De Geest, May 15 1998

Also, numbers m such that m*(m+1)*(m+2)*(m+3)*(m+4)/(m+(m+1)+(m+2)+(m+3)+(m+4)) is an integer.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Cf. A001622, A032768, A032770, A047209, A047215.

[Floor((5*n - 4)/4) : n in [1..80]]; // Wesley Ivan Hurt, May 30 2016

seq(floor((5*n-4)/4), n=1..69); # Gary Detlefs, Mar 06 2010

Table[Floor[(5n - 4)/4], {n, 80}] (* Wesley Ivan Hurt, May 30 2016 *)

a(n)=5*n\4-1 \\ Charles R Greathouse IV, Jan 02 2025

a(n) = (1/8)*(10*n-11+(-1)^n+2*(-1)^floor(n/2)). - Ralf Stephan, Jun 09 2005
a(n) = floor((5*n-4)/4). - Gary Detlefs, Mar 06 2010
G.f.: x^2*(1+x+2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 30 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (10*n-11+i^(2*n)+(1+i)*I^(-n)+(1-i)*i^n)/8 where i=sqrt(-1).
a(2k) = A047209(k), a(2k-1) = A047215(k). (End)
E.g.f.: (4 + sin(x) + cos(x) + (5*x - 6)*sinh(x) + 5*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 31 2016
Sum_{n>=2} (-1)^n/a(n) = log(5)/4 + 3*sqrt(5)*log(phi)/10 - sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 10 2021

Better description from Michael Somos, Jun 08 2000

cp's OEIS Frontend

A032768 a(n) = floor( n(n+1)(n+2)(n+3)(n+4) / (n+(n+1)+(n+2)+(n+3)+(n+4)) ).

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