A166114 -id:A166114 - cp's OEIS frontend

A166122 a(n) = (7-(-5)^n)/6.

1, 2, -3, 22, -103, 522, -2603, 13022, -65103, 325522, -1627603, 8138022, -40690103, 203450522, -1017252603, 5086263022, -25431315103, 127156575522, -635782877603, 3178914388022, -15894571940103, 79472859700522

Offset: 0

Philippe Deléham, Oct 07 2009

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-4,5).

Cf. A084222, A084247, A166114.

LinearRecurrence[{-4,5},{1,2},30] (* Harvey P. Dale, Mar 10 2016 *)
Table[(7 - (-5)^n)/6, {n, 24}] (* or *)
CoefficientList[Series[(1 + 6 x)/(1 + 4 x - 5 x^2), {x, 0, 24}], x] (* Michael De Vlieger, Apr 27 2016 *)

a(n) = 5*a(n-2) - 4*a(n-1), a(0)= 1, a(1)= 2, for n>1.
a(n) = 7-5*a(n-1), a(0)=1.
a(n) = a(n-1)+(-5)^(n-1), a(0)=1.
O.g.f.: (1+6*x)/(1+4*x-5*x^2).
E.g.f.: (7*exp(x)-exp(-5*x))/6.

A166124 Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

Original entry on oeis.org

1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2

Offset: 0

Philippe Deléham, Oct 07 2009

			Triangle begins :
1 ;
0,2 ;
0,1,2 ;
0,1,1,2 ;
0,1,1,1,2 ;
0,1,1,1,1,2 ;
0,1,1,1,1,1,2 ; ...

Sum_{k, 0<=k<=n} T(n,k)*x^(n-k)= A166122(n), A166114(n), A084222(n), A084247(n), A000034(n), A040000(n), A000027(n+1), A000079(n), A007051(n), A047849(n), A047850(n), A047851(n), A047852(n), A047853(n), A047854(n), A047855(n), A047856(n) for x= -5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11 respectively.
Sum_{k, 0<=k<=n} T(n,k)*x^k= A000007(n), A000027(n+1), A033484(n), A134931(n), A083597(n) for x= 0,1,2,3,4 respectively.
T(n,k)= A166065(n,k)/2^(n-k).
G.f.: (1-x+x*y)/(1-x-x*y+x^2*y). - Philippe Deléham, Nov 09 2013
T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 09 2013

cp's OEIS Frontend

A166122 a(n) = (7-(-5)^n)/6.

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A166124 Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

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