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Sum of terms within one periodic pattern of that sequence representing the digital sum analog base n of the Fibonacci recurrence.
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%I #11 Jul 10 2015 19:56:48

%S 1,2,8,30,24,120,156,126,96,234,640,88,264,416,700,630,352,680,468,

%T 304,1200,294,572,1150,528,2600,2288,1998,1176,290,3660,806,1344,1122,

%U 1360,2870,792,2960,532,2262,2400,1722,1764,3870,1056,5490,2300,1598

%N Sum of terms within one periodic pattern of that sequence representing the digital sum analog base n of the Fibonacci recurrence.

%C The respective period lengths are given by A001175(n-1) (which is the Pisano period to n-1) for n>=2.

%e a(3)=8 since the digital sum analog base 3 of the Fibonacci sequence is 0,1,1,2,3,3,2,3,3,... where the pattern {2,3,3} is the periodic part (see A131294) and sums up to 2+3+3=8. a(4)=30 because the pattern base 4 is {2,3,5,5,4,3,4,4} (see A131295) which sums to 30.

%Y Cf. A000045, A131319, A131320.

%Y See A010073, A010074, A010075, A010076, A010077, A131294, A131295, A131296, A131297 for the definition of the digital sum analog of the Fibonacci sequence (in different bases).

%K nonn,base

%O 1,2

%A _Hieronymus Fischer_, Jul 03