cp's OEIS Frontend

A359251 Sum of terms in an odd-even expansion of n.

%I A359251 #26 Apr 17 2023 07:50:59
%S A359251 2,3,10,11,14,15,32,33,36,37,60,61,64,65,110,111,114,115,124,125,128,
%T A359251 129,176,177,180,181,234,235,238,239,342,343,346,347,356,357,360,361,
%U A359251 380,381,384,385,470,471,474,475,578,579,582,583,592,593,596,597,622,623,626,627,792,793,796,797
%N A359251 Sum of terms in an odd-even expansion of n.
%C A359251 n stands alone in the first row, and then each row expands to a new row as follows.
%C A359251 An even number 2b >= 2 or an odd number 2c+1 >= 3 expands into cells below, below left, and below right, as follows:
%C A359251         even           odd
%C A359251          2b            2c+1
%C A359251        b  0  b        c  1  c
%C A359251 When expansions overlap, the values add together in the new cells.
%C A359251 Any 0 or 1 does not expand and expansions end when a row of only 0's and 1's is reached.
%C A359251 This last row is 1,1,1 when n=3 and otherwise always 1,0,1.
%C A359251 a(n) is the sum of all cells in all rows, excluding the starting n itself.
%e A359251 For n = 4:
%e A359251       4       initial row
%e A359251     2 0 2
%e A359251   1 0 2 0 1
%e A359251     1 0 1     last row
%e A359251   a(4) = (2+2) + (1+2+1) + (1+1).
%e A359251 For n = 8:
%e A359251         8
%e A359251       4 0 4
%e A359251     2 0 4 0 2
%e A359251   1 0 3 0 3 0 1
%e A359251     1 1 2 1 1
%e A359251       1 0 1
%e A359251   a(8) = (4+4) + (2+4+2) + (1+3+3+1) + (1+1+2+1+1) + (1+1) = 32.
%K A359251 nonn,easy
%O A359251 2,1
%A A359251 _Moosa Nasir_, Dec 22 2022