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A141516
The main diagonal of the array of A141425 and its higher order differences.
1
1, 2, 1, -7, -23, -1, 7, -103, -251, -133, -149, -1387, -3143, -3001, -4913, -19663, -42611, -55693, -101549, -291667, -612863, -960001, -1831433, -4460023, -9185771, -15980053, -31162949, -69500347, -141392183, -261261001
OFFSET
0,2
COMMENTS
The sequence A141425 and higher order differences in subsequent rows starts (see A141533):
1, 2, 4, 5, 7, 8, 1, 2, 4, 5, 7, 8, 1, 2, 4,...
1, 2, 1, 2, 1,-7, 1, 2, 1, 2, 1,-7, 1, 2, 1, 2,...
1,-1, 1, -1, -8, 8, 1,-1, 1, -1, -8, 8, 1, -1,..
-2, 2,-2, -7, 16,-7,-2, 2,-2, -7, 16,-7, -2,..
4,-4,-5, 23,-23, 5, 4,-4,-5, 23,-23, 5, 4,..
-8,-1,28,-46, 28,-1,-8,-1,28,-46, 28,-1,..
Reading downwards the main diagonal of this array defines the sequence.
FORMULA
a(n) = ( -3*(-1)^n -2^n +3*(-1)^(floor((n-1)/2))*A108411(n) )/2, n>0. - R. J. Mathar, Mar 08 2011
a(2n)+a(2n+1)= -A002023(n-1) = -3*A081294(n), n>0.
a(4n)+a(4n+1)+a(4n+2)+a(4n+3) = -120*16^(n-1), n>0.
a(4n+2)+a(4n+3)+a(4n+4)+a(4n+5) = -30*A001025(n).
G.f. x*(-2+x+6*x^2+21*x^3) / ( (2*x-1)*(1+x)*(3*x^2+1) ). - R. J. Mathar, Mar 08 2011
MAPLE
A108411 := proc(n) 3^floor(n/2) ; end proc:
A141516 := proc(n) if n = 0 then 1; else (-3*(-1)^n-2^n+3*(-1)^(floor((n-1)/2))*A108411(n))/2 ; end if; end proc: # R. J. Mathar, Mar 08 2011
MATHEMATICA
LinearRecurrence[{1, -1, 3, 6}, {1, 2, 1, -7, -23}, 30] (* Harvey P. Dale, Nov 23 2022 *)
CROSSREFS
Sequence in context: A012893 A013075 A009281 * A235378 A214327 A320519
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Aug 11 2008
STATUS
approved