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

Author

Patrick Okolo Edeogu, Oct 20 2015

Keywords

• nonn

Comments

The digits are any nonnegative integers. The value of the minimal sum of digits is given by A007895. The sequence of those numbers where this sequence has value 1 is A256133.

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.

Crossrefs

Cf. A000045, A007895, A256133.

Programs

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):