A168148 Row sums of triangle in A168030.
1, 1, 2, 2, 3, 4, 4, 3, 6, 6, 6, 4, 6, 7, 10, 6, 11, 12, 10, 6, 8, 8, 12, 8, 12, 11, 18, 12, 13, 16, 20, 11, 22, 22, 18, 12, 14, 14, 16, 10, 14, 12, 24, 16, 16, 18, 22, 12, 22, 23, 34, 20, 25, 28, 26, 17, 30, 26, 38, 24, 26, 31, 42, 22, 43, 44, 34, 22, 28, 26, 30, 20, 26
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
Programs
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Mathematica
t[n_, k_]:= t[n, k]= If[k<0 || k>n, 0, If[k==0, 1, If[n<=2*k, t[n, n-k -1] + t[n-1,k], t[n,n-k] + t[n-1,k]]]]; (* A118340 *) Table[Sum[Mod[t[n, k], 2], {k,0,n}], {n,0,80}] (* G. C. Greubel, Jan 12 2023 *)
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SageMath
@CachedFunction def t(n, k): # t = A118340 if (k<0 or k>n): return 0 elif (k==0): return 1 elif (n>2*k): return t(n, n-k) + t(n-1, k) else: return t(n, n-k-1) + t(n-1, k) def A168148(n): return sum( t(n,k)%2 for k in range(n+1)) [A168148(n) for n in range(81)] # G. C. Greubel, Jan 12 2023
Formula
From G. C. Greubel, Jan 12 2023: (Start)
a(n) = Sum_{k=0..n} A168030(n, k).
a(n) = Sum_{k=0..n} (A118340(n, k) mod 2). (End)
Extensions
Terms a(16) onward added by G. C. Greubel, Jan 12 2023