A245548 Number of distinct sum representations of n by Fibonacci numbers with minimal digit sum.
1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1, 1, 2, 2, 3, 2, 1, 1, 3, 1, 4, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 5, 1, 1, 1, 3, 4, 1, 4, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 2, 2, 2, 3, 5, 2, 5, 2, 1, 1, 1, 1, 2, 3, 4, 3, 1, 1, 4, 1, 5
Offset: 1
Keywords
Examples
a(12) = 3 because 12 = 8 + 3 + 1 = 8 + 2 + 2 = 5 + 5 + 2 has three distinct representations.
Links
- M. Drmota and M. Gajdosik, The parity of the sum of digits function of generalized Zeckendorf expansions, The Fibonacci Quarterly, 36:1 (1988), pp. 3-19.
Programs
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Maple
L:=[1,2,3,5,8,13,21,34,55]; LC:=[1,1,1,2,1,2,1,1,1]:LS:=[1,1,1,2,1,2,2,1,2]: for n from 10 to 88 do: ct:=0: ss:=n: sm:=n: b0:=1: b1:=2: b2:=3: b3:=4: b4:=trunc(n/L[5]): b5:=trunc(n/L[6]): b6:=trunc(n/L[7]):b7:=trunc(n/L[8]):b8:=trunc(n/L[9]): > for n0 from 0 to b0 do:for n1 from 0 to b1 do: for n2 from 0 to b2 do:for n3 from 0 to b3 do: for n4 from 0 to b4 do: for n5 from 0 to b5 do: for n6 from 0 to b6 do: > for n7 from 0 to b7 do:for n8 from 0 to b8 do: if n=n0*L[1]+n1*L[2]+n2*L[3]+n3*L[4]+n4*L[5]+n5*L[6]+n6*L[7]+n7*L[8]+n8*L[9] then ss:=n0+n1+n2+n3+n4+n5+n6+n7+n8:fi: > if sm>ss then sm:=ss: fi: od:od:od:od:od:od:od:od:od:for n0 from 0 to b0 do:for n1 from 0 to b1 do: for n2 from 0 to b2 do:for n3 from 0 to b3 do: > for n4 from 0 to b4 do:for n5 from 0 to b5 do:for n6 from 0 to b6 do: > for n7 from 0 to b7 do:for n8 from 0 to b8 do: > if n=n0*L[1]+n1*L[2]+n2*L[3]+n3*L[4]+n4*L[5]+n5*L[6]+n6*L[7]+n7*L[8]+n8*L[9] then st:=n0+n1+n2+n3+n4+n5+n6+n7+n8: if st=sm then ct:=ct+1: fi:fi: od;od:od:od:od:od:od:od:od: LS:=[op(LS),sm]: LC:=[op(LC),ct]: od: print(LC):
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