A124625 -id:A124625 - cp's OEIS frontend

A088439 a(3n) = 3n, otherwise a(n) = 1.

0, 1, 1, 3, 1, 1, 6, 1, 1, 9, 1, 1, 12, 1, 1, 15, 1, 1, 18, 1, 1, 21, 1, 1, 24, 1, 1, 27, 1, 1, 30, 1, 1, 33, 1, 1, 36, 1, 1, 39, 1, 1, 42, 1, 1, 45, 1, 1, 48, 1, 1, 51, 1, 1, 54, 1, 1, 57, 1, 1, 60, 1, 1, 63, 1, 1, 66, 1, 1, 69, 1, 1, 72, 1, 1, 75, 1, 1, 78, 1, 1, 81, 1, 1, 84, 1, 1, 87, 1, 1, 90, 1, 1

Offset: 0

Roger L. Bagula, Nov 09 2003

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Cf. A011655, A079978, A088440, A175676, A124625.

[n mod 3 eq 0 select n else 1: n in [0..100]];  // Bruno Berselli, Mar 11 2011

Table[If[Divisible[n,3],n,1],{n,0,100}] (* or *) LinearRecurrence[ {0,0,2,0,0,-1},{0,1,1,3,1,1},100] (* Harvey P. Dale, Jun 18 2018 *)

def A088439(n): return 1 if (n%3) else n
[A088439(n) for n in range(121)] # G. C. Greubel, Dec 05 2022

From Bruno Berselli, Mar 11 2011: (Start)
G.f.: x*(1+x+3*x^2-x^3-x^4)/(1-x^3)^2.
a(n) = n^A079978(n).
a(n) = 3*A175676(n-1) + A011655(n) for n>0. (End)
E.g.f.: (1/3)*(x+2)*exp(x) - (2/3)*exp(-x/2)*( cos(sqrt(3)*x/2) + x*sin((Pi + 3*sqrt(3)*x)/6) ). - G. C. Greubel, Dec 05 2022

A131805 Row sums of triangular array T: T(j,k) = -(k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.

Original entry on oeis.org

0, -1, 1, 0, 4, 3, 9, 8, 16, 15, 25, 24, 36, 35, 49, 48, 64, 63, 81, 80, 100, 99, 121, 120, 144, 143, 169, 168, 196, 195, 225, 224, 256, 255, 289, 288, 324, 323, 361, 360, 400, 399, 441, 440, 484, 483, 529, 528, 576, 575, 625, 624, 676, 675, 729, 728, 784, 783, 841

Offset: 0

Klaus Brockhaus, Jul 18 2007

Interleaving of A000290 and A067998 (starting at second term).
First differences are -1, 2, -1, 4, -1, 6, -1, 8, -1, 10, ...: a(n+1) - a(n) = (-1)^(n+1)*A124625(n+2).
Main diagonal of T is in A001057, antidiagonal sums are in A131804.

			First seven rows of T are
[ 0 ],
[ 0, -1 ],
[ 0, -1, 2 ],
[ 0, -1, 3, -2 ],
[ 0, -1, 4, -2, 3 ],
[ 0, -1, 5, -2, 4, -3 ],
[ 0, -1, 6, -2, 5, -3, 4 ]

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A000290 (n^2), A067998 (n^2-2*n), A124625, A001057, A131804.

Cf. A131118.

m:=59; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do for k:=2 to j do if k mod 2 eq 0 then M[j, k]:= -k div 2; else M[j, k]:=j-(k div 2); end if; end for; end for; [ &+[ M[j, k]: k in [1..j] ]: j in [1..m] ];

m:=29; &cat[ [ n^2, n^2-1 ]: n in [0..m] ];

makelist((2*n*(n-1)+(2*n+3)*(-1)^n-3)/8,n,0,58); /* Bruno Berselli, Mar 27 2012 */

{m=58; for(n=0, m, r=n%2; print1(((n-r)/2)^2-r, ","))}

a(0) = 0; a(n) = a(n-1) - (n mod 2) + n*(1 - (n mod 2)) for n > 0.
G.f.: x*(-1+2*x+x^2)/((1-x)^3*(1+x)^2).
a(n) = -A131118(2n) = (2n(n-1)+(2n+3)(-1)^n-3)/8. - Bruno Berselli, Mar 27 2012

A216369 a(n) = !(n-1) mod n.

Original entry on oeis.org

0, 0, 1, 2, 4, 2, 6, 6, 1, 6, 1, 2, 10, 8, 4, 6, 13, 8, 9, 6, 13, 10, 21, 14, 14, 16, 10, 22, 17, 26, 2, 6, 1, 4, 34, 26, 5, 10, 10, 6, 4, 8, 16, 10, 19, 2, 18, 38, 48, 36, 13, 42, 13, 44, 34, 22, 28, 12, 28, 26, 22, 60, 55, 38, 49, 32, 65, 38, 67, 36, 68, 62

Offset: 1

Michel Lagneau, Sep 05 2012

nonn

!n is a subfactorial number (A000166).

			a(7)=6 because !(7-1) = 265, and 265 == 6 mod 7.

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Cf. A000166, A124625.

with(numtheory): f:=n->sum(n!*(((-1)^k)*1/k!), k=0..n):for n from 1 to 150 do:  x:=irem(f(n-1),n): printf(`%d, `, x):od:

cp's OEIS Frontend

A088439 a(3n) = 3n, otherwise a(n) = 1.

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A131805 Row sums of triangular array T: T(j,k) = -(k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.

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A216369 a(n) = !(n-1) mod n.

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