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A106345 Diagonal sums of number triangle A106344. 3
1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 2, 0, 3, 2, 3, 1, 3, 2, 2, 1, 2, 1, 3, 1, 2, 2, 3, 0, 5, 3, 5, 2, 4, 3, 4, 1, 5, 3, 4, 2, 3, 2, 3, 1, 3, 2, 4, 1, 4, 3, 3, 1, 4, 2, 5, 2, 3, 3, 5, 0, 8, 5, 8, 3, 7, 5, 6, 2, 7, 4, 7, 3, 5, 4, 6, 1, 8, 5, 7, 3, 6, 4, 5, 2, 5, 3, 5, 2, 4, 3, 4, 1, 5, 3, 6, 2, 5, 4, 5, 1, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

This is a "bow" sequence, a companion to A281185. - N. J. A. Sloane, Apr 26 2017

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..25000

Melissa Dennison, On Properties of the General Bow Sequence, J. Int. Seq., Vol. 22 (2019), Article 19.2.7.

FORMULA

a(n)=sum{k=0..floor(n/2), (binomial(k, n-2k) mod 2)}.

MAPLE

f:=proc(n) option remember;

if n=0 then 0

elif n=1 then 0

elif n=2 then 1

else

   if n mod 2 = 0 then f(n/2)+f(1+n/2) else f((n-1)/2) fi;

fi;

end;

[seq(f(n), n=2..150)]; # (Note that with this recurrence, we list the values starting at n = 2.  N. J. A. Sloane, Apr 26 2017

PROG

(Python)

a = [0]*(104*2)

a[1]=1

for n in range(1, 104):

    a[2*n  ]=a[n-1]

    a[2*n+1]=a[n]+a[n+1]

    print str(a[n])+', ',

# Alex Ratushnyak, Jul 04 2012

CROSSREFS

Cf. A002487, A281185.

Sequence in context: A159847 A257886 A144477 * A319395 A194636 A286299

Adjacent sequences:  A106342 A106343 A106344 * A106346 A106347 A106348

KEYWORD

nonn,look,easy,changed

AUTHOR

Paul Barry, Apr 29 2005

STATUS

approved

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Last modified May 23 05:25 EDT 2019. Contains 323508 sequences. (Running on oeis4.)