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A115634
Expansion of (1-4*x^2)/(1-x^2).
3
1, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0, -3, 0
OFFSET
0,3
COMMENTS
Row sums of number triangle A115633.
FORMULA
a(n) = 4*0^n - 3*(1 + (-1)^n)/2.
a(n) = Sum_{k=0..n} A115633(n, k).
From G. C. Greubel, Nov 23 2021: (Start)
a(n) = 1 if n = 0, otherwise a(n) = -A010674(n-1).
E.g.f.: 4 - 3*cosh(x). (End)
MATHEMATICA
Join[{1}, -3*Mod[Range[100] -1, 2]] (* G. C. Greubel, Nov 23 2021 *)
CoefficientList[Series[(1-4x^2)/(1-x^2), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 1}, {1, 0, -3}, 100] (* or *) PadRight[{1}, 100, {-3, 0}] (* Harvey P. Dale, Dec 06 2024 *)
PROG
(Magma) [4*0^n -3*(1+(-1)^n)/2: n in [0..100]]; // G. C. Greubel, Nov 23 2021
(Sage) [1]+[-3*((n-1)%2) for n in (1..100)] # G. C. Greubel, Nov 23 2021
CROSSREFS
Sequence in context: A334040 A273128 A183035 * A010674 A021037 A053387
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jan 27 2006
STATUS
approved