

A104862


First differences of A014292.


13



0, 1, 1, 1, 1, 0, 2, 5, 9, 13, 15, 12, 0, 25, 65, 117, 169, 196, 158, 3, 321, 841, 1519, 2200, 2560, 2079, 79, 4121, 10881, 19720, 28638, 33435, 27351, 1547, 52895, 140772, 256000, 372775, 436655, 359763, 26871
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OFFSET

0,7


COMMENTS

Real part of the sequence of complex numbers defined by c(n) = c(n1) + i*c(n2) for n > 1, c(0) = 1, c(1) = 1.
a(n) = real part of the sequence b of quaternions defined by b(0)=1, b(1)=1, b(n) = b(n1) + b(n2)*(0,s,s,s) where s = 1/sqrt(3).


LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..6285


FORMULA

G.f.: Re(1/(1xix^2)) = (1x)/(12x+x^2+x^4).  Paul Barry, Apr 25 2005
a(n) = Sum_{k=0..floor(n/2)} C(nk, k)*cos(Pi*k/2).  Paul Barry, Apr 25 2005
a(0)=0, a(1)=1, a(n+1) = a(n)  Sum_{k=0..n3} a(k).  Alex Ratushnyak, May 03 2012


MATHEMATICA

Differences@ LinearRecurrence[{2, 1, 0, 1}, {0, 0, 1, 2}, 42] (* Michael De Vlieger, Mar 19 2021 *)


PROG

(Python)
a = [0]*1000
a[1]=1
for n in range(1, 55):
print(a[n1], end=", ")
s=sum(a[k] for k in range(n2))
a[n+1] = a[n]s
# from Alex Ratushnyak, May 03 2012


CROSSREFS

Cf. A078001, A014292.
Sequence in context: A218706 A270950 A139405 * A190686 A247986 A259252
Adjacent sequences: A104859 A104860 A104861 * A104863 A104864 A104865


KEYWORD

sign


AUTHOR

Gerald McGarvey, Apr 24 2005


STATUS

approved



